diff --git a/.gitignore b/.gitignore index 242fc3a..6e97b8e 100755 --- a/.gitignore +++ b/.gitignore @@ -7,4 +7,4 @@ docs/ .DS_store .vs/ .vscode/ -Makefile +Makefile \ No newline at end of file diff --git a/Makefile b/Makefile index 0132896..3b3bc77 100755 --- a/Makefile +++ b/Makefile @@ -49,6 +49,12 @@ build: $(OBJECTS) xatu: main/xatu.cpp $(OBJECTS) $(CC) -o bin/$@ $< $(CFLAGS) $(INCLUDE) $(LIBS) +read_screening: main/read_screening.cpp $(OBJECTS) + $(CC) -o bin/$@ $< $(CFLAGS) $(INCLUDE) $(LIBS) + +write_screening: main/write_screening.cpp $(OBJECTS) + $(CC) -o bin/$@ $< $(CFLAGS) $(INCLUDE) $(LIBS) + %: main/%.cpp $(OBJECTS) $(CC) -o bin/$@ $< $(CFLAGS) $(INCLUDE) $(LIBS) diff --git a/README.md b/README.md index 3e706ed..e02fa0e 100755 --- a/README.md +++ b/README.md @@ -19,6 +19,12 @@ Xatu (_eXcitons from ATomistic calcUlations_) is a program and library designed The theory behind the code plus details about the implementation and some usage examples can be found in our paper [Efficient computation of optical excitations in two-dimensional materials with the Xatu code](https://doi.org/10.1016/j.cpc.2023.109001). If you find our paper or the code useful, please consider citing us. +The new version of the code computes the exciton states without the need of any external model parameters through a 2D implementation of the microscopic dielectric function within the random-phase approximation (RPA). The RPA macroscopic dielectric function faithfully reproduces that from first-principles calculations. Both strict 2D or quasi-2D calculations can be used to compute the dielectric function and the excitons. The theory behind this new version can be found in the paper [Microscopic screening theory for excitons in two-dimensional materials: A bridge between effective models and _ab initio_ descriptions](https://arxiv.org/abs/2603.10966). If you find the paper or the code useful, please consider citing it. + +

+ +

+ ## Installation Xatu is built upon the Armadillo C++ library for linear algebra, which is also based on the standard libraries por linear algebra, namely BLAS, LAPACK and ARPACK. ### Ubuntu 22.04 LTS native and WSL diff --git a/data/hBN_DFT_HSE06_Gamma_K_q_points.dat b/data/hBN_DFT_HSE06_Gamma_K_q_points.dat new file mode 100755 index 0000000..3f81bdf --- /dev/null +++ b/data/hBN_DFT_HSE06_Gamma_K_q_points.dat @@ -0,0 +1,101 @@ +0. 0. 0. +0.023382695976871922 0.013500005816626184 0. +0.046765391953743844 0.027000011633252368 0. +0.07014808793061576 0.04050001744987856 0. +0.09353078390748769 0.054000023266504736 0. +0.11691347988435961 0.06750002908313092 0. +0.14029617586123153 0.08100003489975711 0. +0.16367887183810345 0.0945000407163833 0. +0.18706156781497538 0.10800004653300947 0. +0.2104442637918473 0.12150005234963566 0. +0.23382695976871923 0.13500005816626184 0. +0.2572096557455911 0.14850006398288804 0. +0.28059235172246305 0.16200006979951423 0. +0.303975047699335 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-0.0000163 -0.0290652 -0.0000326 -0.0456239 -0.0000512 0.9826054 -0.0000000 -0.0196204 0.0000000 + -0.0624745 -0.0000350 0.0193721 -0.0012346 0.0463012 -0.0029507 0.0143333 0.0009271 0.0194224 0.0012563 0.0465195 0.0030288 0.0143265 -0.0009191 -0.0221311 -0.0000124 -0.0327844 -0.0000184 -0.0327843 -0.0000368 -0.0514619 -0.0000577 -0.0196204 -0.0000000 0.9778690 -0.0000000 \ No newline at end of file diff --git a/epsilon_vs_q_hBN.jpg b/epsilon_vs_q_hBN.jpg new file mode 100644 index 0000000..505723b Binary files /dev/null and b/epsilon_vs_q_hBN.jpg differ diff --git a/examples/excitonconfig/hBN_reciprocal.txt b/examples/excitonconfig/hBN_reciprocal.txt index 394683d..e880463 100644 --- a/examples/excitonconfig/hBN_reciprocal.txt +++ b/examples/excitonconfig/hBN_reciprocal.txt @@ -3,11 +3,12 @@ hBN_N30 # ncells ! Number of unit cells along each direction -40 -# reciprocal -5 +20 +# gcutoff +3.0 # bands 1 # Dielectric 1 1 10 -# \ No newline at end of file +# percentage +0 \ No newline at end of file diff --git a/examples/material_models/DFT/MoS2_HSE06.outp b/examples/material_models/DFT/MoS2_HSE06.outp new file mode 100644 index 0000000..2d43243 --- /dev/null +++ b/examples/material_models/DFT/MoS2_HSE06.outp @@ -0,0 +1,24836 @@ +date Thu 28 Aug 12:23:25 CEST 2025 +master hostname lian.fmc.uam.es +system Linux lian.fmc.uam.es 4.18.0-513.11.1.el8_9.x86_64 #1 SMP Wed Jan 10 22:58:54 UTC 2024 x86_64 x86_64 x86_64 GNU/Linux +user palacios +output data in /home/palacios/MoS2/MoS2.outp +properties in /home/palacios/CRYSTAL23OMP/bin/Linux-ifx_i64_omp/v1.0.1 +input data in /home/palacios/MoS2/MoS2.d3 +temporary directory /home/palacios/scratch/tmp_p1931403_palacios +wave function data from /home/palacios/MoS2/MoS2.f9 +wave function formatted data from /home/palacios/MoS2/MoS2.f98 +BASISSET +2 +60 50 +64 50 +END + + + ******************************************************************************* + * * + * CRYSTAL23 * + * public : 1.0.1 - October 2022 * + * HTTP://WWW.CRYSTAL.UNITO.IT * + * * + * MAIN AUTHORS * + * * + * R. DOVESI(1,11), V.R. SAUNDERS(2), C. ROETTI(1,11), R. ORLANDO(1,11), * + * C.M. ZICOVICH-WILSON(1,3), F. PASCALE(4), B. CIVALLERI(1,11), * + * K. DOLL(5), N.M. HARRISON(6), I.J. BUSH(7), Ph. D'ARCO(8), * + * M. LLUNELL(9), M. CAUSA'(10), Y. NOEL(8), L. MASCHIO(1,11), A. ERBA(1,11) * + * M. RE'RAT(14), S. CASASSA(1,11), B.G. SEARLE(2), J.K. DESMARAIS(1) * + * * + * CONTRIBUTIONS TO THE CODE HAVE ALSO BEEN GIVEN BY * + * * + * M. FERRABONE(1,11), M. DE LA PIERRE(1,11), M. FERRERO(1,11), * + * J. BAIMA(1,11), E. ALBANESE(1,11), M.F. PEINTINGER(12), R. BAST(13), * + * B. KIRTMAN(15), V. LACIVITA(1,11), R. DEMICHELIS(1,16) * + * G. BRANDEBURG(17), S. SALUSTRO(1,11), G. SANSONE(1,11) * + * M.T. RUGGIERO(18), L.E. DAGA(1), L. DONA'(1), A. COSSARD(1) * + * * + * (1) THEORETICAL CHEMISTRY GROUP - UNIVERSITA' DI TORINO - TORINO (ITALY) * + * (2) SCIENTIFIC COMPUTING DEPARTMENT - STFC DARESBURY (UK) * + * (3) UNIVERSIDAD AUTONOMA DEL ESTADO DE MORELOS - CUERNAVACA (MEXICO) * + * (4) UNIVERSITE' DE LORRAINE - NANCY (FRANCE) * + * (5) UNIVERSITAET STUTTGART- STUTTGART (GERMANY) * + * (6) IMPERIAL COLLEGE - LONDON (UK) * + * (7) SCIENTIFIC COMPUTING DEPARTMENT - STFC RAL (UK) * + * (8) UPMC - SORBONNE UNIVERSITES - PARIS (FRANCE) * + * (9) UNIVERSIDAD DE BARCELONA - BARCELONA (SPAIN) * + *(10) UNIVERSITA' DI NAPOLI "FEDERICO II" - NAPOLI (ITALY) * + *(11) NIS - NANOSTRUCTURED INTERFACES AND SURFACES - TORINO (ITALY) * + *(12) MPI FUER CHEMISCHE ENERGIEKONVERSION - MUELHEIM AN DER RUHR (GERMANY) * + *(13) UNIVERSITY OF TROMSO - TROMSO (NORWAY) * + *(14) UNIVERSITE' DE PAU ET DES PAYS DE L'ADOUR - PAU (FRANCE) * + *(15) UNIVERSITY OF CALIFORNIA SANTA BARBARA - SANTA BARBARA (USA) * + *(16) CURTIN UNIVERSITY - PERTH (AUSTRALIA) * + *(17) UNIVERSITY COLLEGE LONDON - LONDON (UK) * + *(18) UNIVERSITY OF VERMONT - BURLINGTON (USA) * + * * + ******************************************************************************* + EEEEEEEEEE STARTING DATE 28 08 2025 TIME 12:23:25.6 + INFORMATION **** SET_MPP **** PCRYSTAL CALCULATION + + ******************************************************************************* + MoS2 + CRYSTAL - PROPERTIES - TYPE OF CALCULATION : RESTRICTED CLOSED SHELL + ******************************************************************************* + KOHN-SHAM HAMILTONIAN + + (EXCHANGE)[CORRELATION] FUNCTIONAL:(HSE06 SR/GGA)[PERDEW-BURKE-ERNZERHOF] + + RANGE-SEPARATED HYBRID FUNCTIONAL + OMEGA (SHORT-RANGE)[LONG-RANGE]:( 0.1100)[ 0.0000] + + HYBRID EXCHANGE - PERCENTAGE OF FOCK EXCHANGE 25.0000 + + DIRECT LATTICE VECTOR COMPONENTS (ANGSTROM) + 2.73664 -1.58000 0.00000 + 0.00000 3.16000 0.00000 + 0.00000 0.00000 500.00000 + + LATTICE PARAMETERS (ANGSTROM AND DEGREES) - PRIMITIVE CELL + A B C ALPHA BETA GAMMA VOLUME + 3.16000 3.16000 500.00000 90.0000 90.0000 120.0000 8.64778 + ******************************************************************************* + N. OF ATOMS PER CELL 3 COULOMB OVERLAP TOL (T1) 10** -6 + NUMBER OF SHELLS 24 COULOMB PENETRATION TOL (T2) 10** -6 + NUMBER OF AO 62 EXCHANGE OVERLAP TOL (T3) 10** -6 + N. OF ELECTRONS PER CELL 46 EXCHANGE PSEUDO OVP (F(G)) (T4) 10** -6 + CORE ELECTRONS PER CELL 20 EXCHANGE PSEUDO OVP (P(G)) (T5) 10** -12 + N. OF SYMMETRY OPERATORS 12 POLE ORDER IN MONO ZONE 4 + CORE PSEUDO POTENTIAL TOL. ON PSEUDO (TP) 10**- 6 + ******************************************************************************* + ATOM N.AT. SHELL X(A) Y(A) Z(A) EXAD N.ELECT. + ******************************************************************************* + 1 242 MO 8 0.000 0.000 0.000 1.055E+00 11.879 + 2 16 S 8 -1.824 -0.000 1.585 1.500E-01 17.060 + 3 16 S 8 -1.824 -0.000 -1.585 1.500E-01 17.060 + ******************************************************************************* + DE(K) 0.000E+00 ENERGY LEVEL SHIFTING 0.00000 + TOTAL ENERGY -8.6396667462575E+02 CONVERGENCE ON ENER -2.524E-11 + KIN. ENERGY 8.1734951339200E+02 VIR. COEFF. 9.99290692E-01 + N. OF SCF CYCLES 12 FERMI ENERGY -0.225E+00 + WEIGHT OF F(I) IN F(I+1) 70 + SHRINK. FACT.(MONKH.) 12 12 1 SHRINKING FACTOR(GILAT NET) 24 + NUMBER OF K POINTS IN THE IBZ 19 CELL VOLUME (A.U.) 30.881795 + ******************************************************************************* + + GCALCO - MAX INDICES DIRECT LATTICE VECTOR 83 83 0 + NO.OF VECTORS CREATED 6999 STARS 503 RMAX 262.54387 BOHR + TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT gordsh1 TELAPSE 0.02 TCPU 0.02 + + MATRIX SIZE: P(G) 63056, F(G) 14736, P(G) IRR 5012, F(G) IRR 2661 + MAX G-VECTOR INDEX FOR 1- AND 2-ELECTRON INTEGRALS 37 + + + CAPPA:IS1 12;IS2 12;IS3 1; K PTS MONK NET 19; SYMMOPS:K SPACE 24;G SPACE 12 + + + ******************************************************************************* + MoS2 + CRYSTAL - PROPERTIES - TYPE OF CALCULATION : RESTRICTED CLOSED SHELL + ******************************************************************************* + KOHN-SHAM HAMILTONIAN + + (EXCHANGE)[CORRELATION] FUNCTIONAL:(HSE06 SR/GGA)[PERDEW-BURKE-ERNZERHOF] + + RANGE-SEPARATED HYBRID FUNCTIONAL + OMEGA (SHORT-RANGE)[LONG-RANGE]:( 0.1100)[ 0.0000] + + HYBRID EXCHANGE - PERCENTAGE OF FOCK EXCHANGE 25.0000 + + DIRECT LATTICE VECTOR COMPONENTS (ANGSTROM) + 2.73664 -1.58000 0.00000 + 0.00000 3.16000 0.00000 + 0.00000 0.00000 500.00000 + + LATTICE PARAMETERS (ANGSTROM AND DEGREES) - PRIMITIVE CELL + A B C ALPHA BETA GAMMA VOLUME + 3.16000 3.16000 500.00000 90.0000 90.0000 120.0000 8.64778 + ******************************************************************************* + N. OF ATOMS PER CELL 3 COULOMB OVERLAP TOL (T1) 10** -6 + NUMBER OF SHELLS 24 COULOMB PENETRATION TOL (T2) 10** -6 + NUMBER OF AO 62 EXCHANGE OVERLAP TOL (T3) 10** -6 + N. OF ELECTRONS PER CELL 46 EXCHANGE PSEUDO OVP (F(G)) (T4) 10** -6 + CORE ELECTRONS PER CELL 20 EXCHANGE PSEUDO OVP (P(G)) (T5) 10** -12 + N. OF SYMMETRY OPERATORS 12 POLE ORDER IN MONO ZONE 4 + CORE PSEUDO POTENTIAL TOL. ON PSEUDO (TP) 10**- 6 + ******************************************************************************* + ATOM N.AT. SHELL X(A) Y(A) Z(A) EXAD N.ELECT. + ******************************************************************************* + 1 242 MO 8 0.000 0.000 0.000 1.055E+00 11.879 + 2 16 S 8 -1.824 -0.000 1.585 1.500E-01 17.060 + 3 16 S 8 -1.824 -0.000 -1.585 1.500E-01 17.060 + ******************************************************************************* + DE(K) 0.000E+00 ENERGY LEVEL SHIFTING 0.00000 + TOTAL ENERGY -8.6396667462575E+02 CONVERGENCE ON ENER -2.524E-11 + KIN. ENERGY 8.1734951339200E+02 VIR. COEFF. 9.99290692E-01 + N. OF SCF CYCLES 12 FERMI ENERGY -0.225E+00 + WEIGHT OF F(I) IN F(I+1) 70 + SHRINK. FACT.(MONKH.) 12 12 1 SHRINKING FACTOR(GILAT NET) 24 + NUMBER OF K POINTS IN THE IBZ 19 CELL VOLUME (A.U.) 30.881795 + ******************************************************************************* + + ******************************************************************************* + LOCAL ATOMIC FUNCTIONS BASIS SET + ******************************************************************************* + ATOM X(AU) Y(AU) Z(AU) N. 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0.0000E+00 + TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT BASISSET TELAPSE 0.04 TCPU 0.04 + ENDPROP + TTTTTTTTTTTTTTTTTTTTTTTTTTTTTT END TELAPSE 0.04 TCPU 0.04 + EEEEEEEEEE TERMINATION DATE 28 08 2025 TIME 12:23:25.6 +Thu 28 Aug 12:23:25 CEST 2025 +Contents of temporary directory: +total 1336 +-rw-rw-r--. 1 palacios palacios 117896 Aug 28 12:23 fort.11 +-rw-rw-r--. 1 palacios palacios 504456 Aug 28 12:23 fort.13 +-rw-rw-r--. 1 palacios palacios 117896 Aug 28 12:23 fort.3 +-rw-rw-r--. 1 palacios palacios 172812 Aug 28 12:23 fort.9 +-rw-rw-r--. 1 palacios palacios 443944 Aug 28 12:23 fort.98 +file fort.98 saved as /home/palacios/MoS2/MoS2.f98 +file fort.13 saved as /home/palacios/MoS2/MoS2.f13 +removing temporary directories /home/palacios/scratch/tmp_p1931403_palacios diff --git a/examples/screeningconfig/MoS2_DFT_screening.txt b/examples/screeningconfig/MoS2_DFT_screening.txt new file mode 100644 index 0000000..64c7033 --- /dev/null +++ b/examples/screeningconfig/MoS2_DFT_screening.txt @@ -0,0 +1,20 @@ +# valence.bands +21 +# conduction.bands +38 +# vectors +0 0 +# momentum +0.3 0.0 0. +# motif.vectors +0 0 +# function +dielectric +# ncell_aux +13 +# spin +false +# gcutoff +3 +# thickness +6.11 \ No newline at end of file diff --git a/examples/screeningconfig/hBN_DFT_screening.txt b/examples/screeningconfig/hBN_DFT_screening.txt new file mode 100644 index 0000000..f2011a6 --- /dev/null +++ b/examples/screeningconfig/hBN_DFT_screening.txt @@ -0,0 +1,20 @@ +# valence.bands +6 +# conduction.bands +63 +# vectors +0 0 +# momentum +0.2 0. 0. +# function +dielectric +# ncell_aux +10 +# spin +false +# isotropic +true +# gcutoff +3.0 +# thickness +3.33 \ No newline at end of file diff --git a/include/xatu/Exciton.hpp b/include/xatu/Exciton.hpp index eb4a5c2..dc095c5 100755 --- a/include/xatu/Exciton.hpp +++ b/include/xatu/Exciton.hpp @@ -39,9 +39,22 @@ class Exciton { double cutoff_; arma::cx_mat HBS_; + // General Screening attributes + int nvalencebands_, nconductionbands_, nrmcbands_; + arma::ivec valencebands_, conductionbands_; + bool isscreeningset = false; + + arma::rowvec q_; + arma::ivec Gs_; + // Flags bool exchange = false; + arma::mat q_points; + + arma::cube eigvalkqStack_test; + std::vector eigveckqStack_test; + // Internals for BSE arma::mat eigvalKStack_, eigvalKQStack_; arma::cx_cube eigvecKStack_, eigvecKQStack_; @@ -75,6 +88,11 @@ class Exciton { // Returns scissor cut value const double& scissor = scissor_; + // List of valence bands used to compute the dielectric function + const arma::ivec& valencebands = valencebands_; + // List of conduction bands used to compute the dielectric function + const arma::ivec& conductionbands = conductionbands_; + const arma::mat& eigvalKStack = eigvalKStack_; const arma::mat& eigvalKQStack = eigvalKQStack_; const arma::cx_cube& eigvecKStack = eigvecKStack_; diff --git a/include/xatu/Exciton.tpp b/include/xatu/Exciton.tpp index c385aaf..adde47a 100755 --- a/include/xatu/Exciton.tpp +++ b/include/xatu/Exciton.tpp @@ -191,7 +191,7 @@ template void Exciton::generateBandDictionary(){ std::map bandToIndex; - for(int i = 0; i < bandList.n_elem; i++){ + for(uint i = 0; i < bandList.n_elem; i++){ bandToIndex[bandList(i)] = i; }; @@ -206,13 +206,13 @@ template void Exciton::printInformation(){ std::cout << std::left << std::setw(30) << "Number of cells: " << ncell << std::endl; std::cout << std::left << std::setw(30) << "Valence bands:"; - for (int i = 0; i < valenceBands.n_elem; i++){ + for (uint i = 0; i < valenceBands.n_elem; i++){ std::cout << valenceBands(i) << "\t"; } std::cout << std::endl; std::cout << std::left << std::setw(30) << "Conduction bands: "; - for (int i = 0; i < conductionBands.n_elem; i++){ + for (uint i = 0; i < conductionBands.n_elem; i++){ std::cout << conductionBands(i) << "\t"; } std::cout << "\n" << std::endl; diff --git a/include/xatu/ExcitonConfiguration.hpp b/include/xatu/ExcitonConfiguration.hpp index 0d51e27..d1e0ab4 100755 --- a/include/xatu/ExcitonConfiguration.hpp +++ b/include/xatu/ExcitonConfiguration.hpp @@ -28,6 +28,8 @@ class ExcitonConfiguration : public ConfigurationBase{ arma::rowvec shift; // Cutoff to be used double cutoff; + // Bool true/false if Gcutoff was/was not found + bool Gcutoff_found = false; // Dielectric constants arma::vec eps = {}; // Screening length @@ -36,7 +38,7 @@ class ExcitonConfiguration : public ConfigurationBase{ double ry; // Screening length double rz; - // Thickness of layer + // Thickness of the 2D system double d; // Calculation mode (either 'realspace' or 'reciprocalspace') std::string mode = "realspace"; @@ -44,19 +46,21 @@ class ExcitonConfiguration : public ConfigurationBase{ bool exchange = false; // Scissor cut to correct the bandgap double scissor = 0.0; - // Number of reciprocal vectors to use in reciprocal space calculation - int nReciprocalVectors = 0; + // G cutoff for reciprocal vectors to use in reciprocal space calculation + double Gc_ReciprocalVectors = 0.0; // Potential to use in direct term std::string potential = "keldysh"; // Potential to use in exchange if active std::string exchangePotential = "keldysh"; // Regularization distance double regularization = 0.0; + // Percentage of norm of k0, where k0 is the k point in the BZ mesh closer to the origin, for regularization + double percentage = 0.5; }; public: configuration excitonInfo; - std::vector supportedPotentials = {"keldysh", "coulomb"}; + std::vector supportedPotentials = {"keldysh", "coulomb", "rpa"}; public: ExcitonConfiguration(); diff --git a/include/xatu/ExcitonTB.hpp b/include/xatu/ExcitonTB.hpp index b38b3ef..54945ff 100644 --- a/include/xatu/ExcitonTB.hpp +++ b/include/xatu/ExcitonTB.hpp @@ -5,14 +5,22 @@ #include "xatu/SystemTB.hpp" #include "xatu/Exciton.hpp" #include "xatu/ExcitonConfiguration.hpp" +#include "xatu/ScreeningConfiguration.hpp" #include "xatu/ResultTB.hpp" - +#include #ifndef constants #define PI 3.141592653589793 #define ec 1.6021766E-19 #define eps0 8.8541878E-12 #endif +/** + *Method to prompt user to continue + *@param message + *@return void +*/ +void continueprompt(std::string); + namespace xatu { // Definitions @@ -42,8 +50,36 @@ class ExcitonTB : public Exciton { arma::cx_cube ftMotifStack; std::complex ftX; arma::mat potentialMat; + double Gc_exciton_ = 10.0; int nReciprocalVectors_ = 1; + // Internals for dielectric function + std::string function_; + arma::ivec Gs_ = {0, 0}; + arma::rowvec q_ = {0.2, 0., 0.}; + uint nGs; + double Gcutoff_ = 3.0; + int Nqpoints = 1; // Number of q points to compute the dielectric function at + double d_ = 0.0; // Effective thickness of the 2D system + uint ncell_aux_ = 10; // Number of unit cells used to compute the dielectric function + uint nk_aux_ = ncell_aux_*ncell_aux_; // Number of k points used to compute the dielectric function + uint g_s_ = 1; // Spin degeneracy + arma::mat kpoints_aux_; // Auxiliar coarser BZ mesh to compute the dielectric function + arma::mat qpoints_list_; + arma::mat trunreciprocalLattice_; + + // Internals for dielectric fucntion + arma::mat eigvalkStack_, eigvalkqStack_; + arma::cx_cube eigveckStack_, eigveckqStack_; + + arma::cx_cube Chimatrix_; + arma::cx_cube epsilonmatrix_; + arma::cx_cube Invepsilonmatrix_; + + double percentage_ = 0; // Percentage of norm of k0, where k0 is the k point in the BZ mesh closer to the origin, for regularization + double W00_at_0_ = 0.0; + arma::rowvec q0_ = {0.2, 0.0, 0.0}; + bool isotropic_ = false; // Is system isotropic public: // Returns dielectric constant of embedding medium @@ -64,7 +100,30 @@ class ExcitonTB : public Exciton { const std::string& mode = mode_; // Return number of reciprocal lattice vectors to use in summations (mode="reciprocalspace") const int& nReciprocalVectors = nReciprocalVectors_; + // Return Gc cutoff for reciprocal lattice vectors to use in summations (mode="reciprocalspace") + const double& Gc_exciton = Gc_exciton_; + // Returns auxiliar coarser BZ mesh to compute the dielectric function + arma::mat& kpoints_aux = kpoints_aux_; + // Returns percentage of norm of k0, where k0 is the k point in the BZ mesh closer to the origin, for regularization + double& percentage = percentage_; + // Returns whether system is isotropic + bool& isotropic = isotropic_; + + // Returns spin degeneracy + uint& g_s = g_s_; + // Returns thickness + double& d = d_; + + // Return momentum to compute the dielectric matrix at + const arma::rowvec& q = q_; + const arma::ivec& Gs = Gs_; + // Return number of cells in each direction used to compute the dielectric function + const uint& ncell_aux = ncell_aux_; + // Return number of k points used to compute the dielectric function + const uint& nk_aux = nk_aux_; + + arma::mat trunLattice_; // ----------------------------------- Methods ----------------------------------- // Constructor & Destructor private: @@ -83,6 +142,9 @@ class ExcitonTB : public Exciton { // Use two files: the mandatory one for system config., and one for exciton config. ExcitonTB(const SystemConfiguration&, const ExcitonConfiguration&); + // Use three files: the mandatory one for system config., one for the screening config. and one for exciton config. + ExcitonTB(const SystemConfiguration&, const ExcitonConfiguration&, const ScreeningConfiguration&); + // Initialize exciton passing directly a System object instead of a file using removed bands ExcitonTB(std::shared_ptr, int ncell = 20, int nbands = 1, int nrmbands = 0, const arma::rowvec& parameters = {1, 5, 1, 1, 1}, const arma::rowvec& Q = {0., 0., 0.}); @@ -91,6 +153,10 @@ class ExcitonTB : public Exciton { ExcitonTB(std::shared_ptr, int ncell = 20, const arma::ivec& bands = {0, 1}, const arma::rowvec& parameters = {1, 5, 1, 1, 1}, const arma::rowvec& Q = {0., 0., 0.}); + // Initialize exciton passing directly a System object instead of a screening + ExcitonTB(const SystemConfiguration&, int ncell, int nbands, int nrmbands, + const arma::rowvec& parameters, const arma::rowvec& Q, const uint ncell_aux, const uint nvbands, const uint ncbands, const double Gcutoff, const double Gc_exciton, const double d, const bool spin = true, const bool isotropic = false); + // ~ExcitonTB(); // Setters @@ -98,8 +164,26 @@ class ExcitonTB : public Exciton { void setParameters(double, double, double, double, double); void setGauge(std::string); void setMode(std::string); - void setReciprocalVectors(int); void setRegularization(double); + void setGcutoff(double); + void setValenceBands(int); + void setConductionBands(int); + void setVectors(int,int); + void setVectors(arma::ivec); + void setPotential(std::string); + void setExchangePotential(std::string); + void setTrunLattice(int,double); + void setq_points_list(arma::mat); + void setPercentage(double); + void setThickness(double); + + // Getters + int getNGs() const; + double getThickness() const; + arma::cx_cube getChiMatrix() const; + arma::cx_cube getInverseDielectricMatrix() const; + std::vector>>> getPolarizabilityMatrix_as_vector() const; + std::vector>>> getInverseDielectricMatrix_as_vector() const; private: // Potentials @@ -109,7 +193,9 @@ class ExcitonTB : public Exciton { potptr selectPotential(std::string); // Fourier transforms - double keldyshFT(arma::rowvec); + double coulomb_2D_FT(const arma::rowvec&) const; + double keldyshFT(arma::rowvec) const; + std::complex rpaFT(int g, int g2, arma::rowvec) const; std::complex motifFourierTransform(int, int, const arma::rowvec&, const arma::mat&, potptr); arma::cx_mat motifFTMatrix(const arma::rowvec&, const arma::mat&, potptr); arma::cx_mat extendMotifFT(const arma::cx_mat&); @@ -121,10 +207,14 @@ class ExcitonTB : public Exciton { std::complex reciprocalInteractionTerm(const arma::cx_vec&, const arma::cx_vec&, const arma::cx_vec&, const arma::cx_vec&, const arma::rowvec&, const arma::rowvec&, - const arma::rowvec&, const arma::rowvec&, int nrcells = 15); + const arma::rowvec&, const arma::rowvec&, + std::string, int nrcells = 15); std::complex blochCoherenceFactor(const arma::cx_vec&, const arma::cx_vec&, const arma::rowvec&, const arma::rowvec&, const arma::rowvec&); + std::complex blochCoherenceFactor(const arma::cx_vec &, const arma::cx_vec &, + const arma::rowvec &, const arma::rowvec &, + const arma::rowvec &, const double) const; // Initializers void initializeExcitonAttributes(int, const arma::ivec&, const arma::rowvec&, const arma::rowvec&); @@ -139,13 +229,33 @@ class ExcitonTB : public Exciton { // Diagonalization ResultTB* diagonalizeRaw(std::string method = "diag", int nstates = 8) override; - public: - // BSE initialization and energies + // Static dielectric function + int fetchReciprocalLatticeVector(arma::rowvec); + std::complex computesinglePolarizabilityMatrixElement(arma::rowvec &, arma::rowvec &, arma::rowvec &); + std::complex compute_2D_PolarizabilityMatrixElement(const arma::rowvec&, const arma::rowvec&, const arma::rowvec&); + std::complex compute_quasi2D_PolarizabilityMatrixElement(const arma::rowvec&, const arma::rowvec&, const arma::rowvec&, const double); + std::complex compute_2D_PolarizabilityMatrixElement(const arma::rowvec&, const arma::rowvec&, const arma::rowvec&, const arma::rowvec&, const double); + std::complex compute_2D_DielectricMatrixElement(const arma::rowvec&, const arma::rowvec&, const arma::rowvec&); + std::complex compute_quasi2D_DielectricMatrixElement(const arma::rowvec &G, const arma::rowvec &G2, const arma::rowvec &q, const double); + + public: + // Static dielectric function, BSE initialization and energies void initializeHamiltonian(); + void initializeScreeningAttributes(const ScreeningConfiguration&); + void initializeScreeningAttributes(const ScreeningConfiguration&, const std::string); + std::complex computesingleDielectricFunctionMatrixElement(); + void computesingleInverseDielectricMatrix(std::string); + void PolarizabilityMesh(); + void compute_2D_DielectricMatrix(); + void compute_2D_DielectricMatrix(std::string); + void augment_2D_DielectricMatrix(double); + void compute_ScreenedPotential_regularization(bool); + void compute_2D_PolarizabilityMatrix(std::string); + void invertDielectricMatrix(); void BShamiltonian(); void BShamiltonian(const arma::imat& basis); std::unique_ptr diagonalize(std::string method = "diag", int nstates = 8); - + // Fermi golden rule double pairDensityOfStates(double, double) const; void writePairDOS(FILE*, double delta, int n = 100); @@ -158,6 +268,21 @@ class ExcitonTB : public Exciton { // Print information void printInformation(); + void printReciprocalLattice(); + + // Write BZ mesh in a file + void writeBZtofile() const; + // Write polarizability matrix in a file + void writePolarizabilityMatrix(std::string) const; + // Read inverse of dielectric matrix in a file + void readInverseDielectricMatrix(std::string); + // Write inverse of dielectric matrix in a file + void writeInverseDielectricMatrix(std::string); // if the user did not compute the inverse dielectric matrix, then the method tries to do it + // Write dielectric matrix in a file + void writeDielectricMatrix(std::string) const; + + // Verifies if potential chosen is 'rpa' and if a screening file was not provided + void verifypotential(); }; } \ No newline at end of file diff --git a/include/xatu/Lattice.hpp b/include/xatu/Lattice.hpp index 6bbefd8..56aece4 100755 --- a/include/xatu/Lattice.hpp +++ b/include/xatu/Lattice.hpp @@ -11,6 +11,12 @@ #define eps0 8.8541878E-12 #endif +/** + *Method to sort rows in a matrix by norm + *@return void +*/ +void sortVectors(arma::mat&); + namespace xatu { /// @brief The Lattice class is designed to hold all information regarding both @@ -24,11 +30,14 @@ class Lattice { int factor_ = 1; double a_, c_, unitCellArea_; arma::mat bravaisLattice_, motif_, unitCellList_; - arma::mat reciprocalLattice_, kpoints_, meshBZ_; + arma::mat kpoints_, meshBZ_; std::map atomToIndex; arma::mat inverseReciprocalMatrix; - // Const references to attributes (read-only) + private: + + + // Const references to attributes (read-only) public: // Returns system dimension const int& ndim = ndim_; @@ -61,8 +70,10 @@ class Lattice { const int& ncells = ncells_; // Reduction factor of Brillouin zone mesh const int& factor = factor_; + // Reciprocal Lattice matrix + arma::mat reciprocalLattice_; - //// Methods + //// Methods protected: Lattice(){}; // Protected so that Lattice can not be initialized (abstract) public: @@ -78,8 +89,9 @@ class Lattice { // Supercells arma::mat truncateSupercell(int, double); - arma::mat truncateReciprocalSupercell(int, double); + arma::mat truncateReciprocalSupercell(double); arma::mat generateCombinations(int n, int ndim, bool centered = false); + arma::imat generateCombinationsGcutoff(double, int); /* Crystal operations */ arma::rowvec rotateC3(const arma::rowvec&); diff --git a/include/xatu/Result.tpp b/include/xatu/Result.tpp index 09f9939..921febf 100755 --- a/include/xatu/Result.tpp +++ b/include/xatu/Result.tpp @@ -403,7 +403,7 @@ void Result::writeRealspaceAmplitude(int stateindex, int holeIndex, template void Result::writeEigenvalues(FILE* textfile, int n){ - if(n > exciton->excitonbasisdim || n < 0){ + if(n > (int)exciton->excitonbasisdim || n < 0){ throw std::invalid_argument("Optional argument n must be a positive integer equal or below basisdim"); } diff --git a/include/xatu/ScreeningConfiguration.hpp b/include/xatu/ScreeningConfiguration.hpp new file mode 100644 index 0000000..9346b09 --- /dev/null +++ b/include/xatu/ScreeningConfiguration.hpp @@ -0,0 +1,62 @@ +#pragma once +#include +#include "xatu/ConfigurationBase.hpp" + +namespace xatu { + +/** + * ScreeningConfiguration is a specialization of ConfigurationBase to parse + * dielectric function configuration files. + */ +class ScreeningConfiguration : public ConfigurationBase{ + + struct configuration { + // Simulation label + std::string label; + // Number of unit cells in the calculation + int ncell; + // Number of valence bands included calculation. + int nvbands = 0; + // Number of conduction bands included calculation. + int ncbands = 0; + // Momentum to compute the dielectric function. + arma::rowvec q = {0.2, 0., 0.}; + // Reduction factor of the BZ mesh. Defaults to 1. + int submeshFactor = 1; + // Pair of reciprocal vectors (G,G') to compute the reciprocal space dielectric function at + arma::ivec Gs = {0, 0}; + // Pair of motif vectors (i,j) to compute the real space dielectric function at + arma::ivec ts = {0, 0}; + // Number of Bravais lattice vectors to use in real space calculation + int nLatticeVectors = 0; + // Gc cutoff for the reciprocal lattice vectors + double Gcutoff = 10.0; + // Regularization distance + double regularization = 0.0; + // Compute dielectric function or polarizability or none + std::string function = "dielectric"; + // Bool that is true/false when the dielectric function is/is not used + bool isscreeningset = "false"; + // Bool that is true/false if the model is spinful/spinless + bool spin = "true"; + // Number of k points in each direction for the auxiliary coarser BZ mesh + int ncell_aux = 17; + // Thickness of the 2D system + double d = 0.0; + // Is system isotropic + bool isotropic = false; + }; + + public: + configuration screeningInfo; + + public: + ScreeningConfiguration(); + ScreeningConfiguration(std::string); + + private: + virtual void parseContent(); + void checkContentCoherence(); +}; + +} \ No newline at end of file diff --git a/main/read_screening.cpp b/main/read_screening.cpp new file mode 100644 index 0000000..2f2fcb3 --- /dev/null +++ b/main/read_screening.cpp @@ -0,0 +1,127 @@ +#include +#include +#include +#include + +using namespace std::chrono; + +// run command: ./read_screening ../examples/material_models/DFT/hBN_base_HSE06.outp ../examples/excitonconfig/hBN_reciprocal.txt ../examples/screeningconfig/hBN_DFT_screening.txt .dat + +int main(int argc, char* argv[]){ + + // Parse console stdin + int n_args = 5; + + if (argc != n_args){ + throw std::invalid_argument("Error: Four input files are expected"); + } + else if (argc < n_args){ + throw std::invalid_argument("Error: At least two input file are required (system config, exciton config, screening config and screening data file)."); + }; + + std::string modelfile = argv[1]; + std::string excitonfile = argv[2]; + std::string screeningfile = argv[3]; + std::string inv_epsilon_file = argv[4]; + + int nstates = 8; + int decimals = 6; + + std::unique_ptr systemConfig; + std::unique_ptr excitonConfig; + std::unique_ptr screeningConfig; + + if (modelfile.find(".outp") != std::string::npos){ + systemConfig.reset(new xatu::CRYSTALConfiguration(modelfile, 100)); + } + else if (modelfile.find(".model") != std::string::npos){ + systemConfig.reset(new xatu::SystemConfiguration(modelfile)); + } else { + throw std::invalid_argument("Error: Unsupported system configuration file format. Use .outp or .model files."); + } + + screeningConfig.reset(new xatu::ScreeningConfiguration(screeningfile)); + excitonConfig.reset(new xatu::ExcitonConfiguration(excitonfile)); + + + xatu::ExcitonTB exciton = xatu::ExcitonTB(*systemConfig, *excitonConfig, *screeningConfig); + + exciton.setMode(excitonConfig->excitonInfo.mode); + + if (modelfile.find(".outp") != std::string::npos){ + exciton.system->setAU(true); // if input model is CRYSTAL + } + + exciton.brillouinZoneMesh(exciton.ncell); + exciton.initializeHamiltonian(); + + exciton.printInformation(); + + exciton.readInverseDielectricMatrix(inv_epsilon_file); + + exciton.BShamiltonian(); + + auto results = exciton.diagonalize("diag", nstates); + + std::cout << "+---------------------------------------------------------------------------+" << std::endl; + std::cout << "| Results |" << std::endl; + std::cout << "+---------------------------------------------------------------------------+" << std::endl; + + xatu::printEnergies(results, nstates, decimals); + + std::cout << "+---------------------------------------------------------------------------+" << std::endl; + std::cout << "| Output |" << std::endl; + std::cout << "+---------------------------------------------------------------------------+" << std::endl; + + std::string output = excitonConfig->excitonInfo.label; + + // --------------------------- Output --------------------------- + bool writeEigvals = true; + if(writeEigvals){ + std::string filename_en = output + ".eigval"; + FILE* textfile_en = fopen(filename_en.c_str(), "w"); + + std::cout << "Writing eigvals to file: " << filename_en << std::endl; + fprintf(textfile_en, "%d\n", excitonConfig->excitonInfo.ncell); + results->writeEigenvalues(textfile_en, nstates); + + fclose(textfile_en); + } + + bool writeStates = true; + if(writeStates){ + std::string filename_st = output + ".states"; + FILE* textfile_st = fopen(filename_st.c_str(), "w"); + + std::cout << "Writing states to file: " << filename_st << std::endl; + results->writeStates(textfile_st, nstates); + + fclose(textfile_st); + } + + bool writeWF = true; + if(writeWF){ + std::string filename_kwf = output + ".kwf"; + FILE* textfile_kwf = fopen(filename_kwf.c_str(), "w"); + + std::cout << "Writing k w.f. to file: " << filename_kwf << std::endl; + for(int stateindex = 0; stateindex < nstates; stateindex++){ + if (excitonConfig->excitonInfo.submeshFactor != 1){ + results->writeReciprocalAmplitude(stateindex, textfile_kwf); + } + else{ + results->writeExtendedReciprocalAmplitude(stateindex, textfile_kwf); + } + } + + fclose(textfile_kwf); + } + + bool writeAbs = true; + if(writeAbs){ + std::cout << "Writing absorption spectrum fo file... " << std::endl; + results->writeAbsorptionSpectrum(); + } + + return 0; +} \ No newline at end of file diff --git a/main/write_screening.cpp b/main/write_screening.cpp new file mode 100644 index 0000000..19f28ba --- /dev/null +++ b/main/write_screening.cpp @@ -0,0 +1,72 @@ +#include +#include +#include +#include + +using namespace std::chrono; + +// run command: ./write_screening ../examples/material_models/DFT/hBN_base_HSE06.outp ../examples/excitonconfig/hBN_test.txt ../examples/screeningconfig/hBN_DFT_screening.txt .dat + +int main(int argc, char* argv[]){ + + // Parse console stdin + + if (argc != 5){ + throw std::invalid_argument("Error: Four input files are expected"); + } + else if (argc < 5){ + throw std::invalid_argument("Error: At least two input file are required (system config, exciton config, screening config and q points file)."); + }; + + std::string modelfile = argv[1]; + std::string excitonfile = argv[2]; + std::string screeningfile = argv[3]; + std::string q_points_file = argv[4]; + + std::unique_ptr systemConfig; + std::unique_ptr excitonConfig; + std::unique_ptr screeningConfig; + + if (modelfile.find(".outp") != std::string::npos){ + systemConfig.reset(new xatu::CRYSTALConfiguration(modelfile, 100)); + } + else if (modelfile.find(".model") != std::string::npos){ + systemConfig.reset(new xatu::SystemConfiguration(modelfile)); + } else { + throw std::invalid_argument("Error: Unsupported system configuration file format. Use .outp or .model files."); + } + + + screeningConfig.reset(new xatu::ScreeningConfiguration(screeningfile)); + excitonConfig.reset(new xatu::ExcitonConfiguration(excitonfile)); + + + xatu::ExcitonTB exciton = xatu::ExcitonTB(*systemConfig, *excitonConfig, *screeningConfig); + exciton.setMode(excitonConfig->excitonInfo.mode); + + if (modelfile.find(".outp") != std::string::npos){ + exciton.system->setAU(true); // if input model is CRYSTAL + } + + std::cout << "+---------------------------------------------------------------------------+" << std::endl; + std::cout << "| Parameters |" << std::endl; + std::cout << "+---------------------------------------------------------------------------+" << std::endl; + + std::cout << "System configuration file: " << modelfile << "\n" << std::endl; + std::cout << "q points file file: " << q_points_file << "\n" << std::endl; + + + exciton.brillouinZoneMesh(exciton.ncell); + exciton.initializeHamiltonian(); + + exciton.compute_2D_DielectricMatrix(q_points_file); + + size_t lastindex = q_points_file.find_last_of("."); + std::string rawname = q_points_file.substr(0, lastindex); + + exciton.invertDielectricMatrix(); + + exciton.writeInverseDielectricMatrix(rawname + "_invepsilon.dat"); + + return 0; +} \ No newline at end of file diff --git a/main/xatu.cpp b/main/xatu.cpp index f4e43c2..9fb265c 100755 --- a/main/xatu.cpp +++ b/main/xatu.cpp @@ -42,10 +42,9 @@ int main(int argc, char* argv[]){ TCLAP::ValuesConstraint allowedMethods(methods); TCLAP::ValueArg methodArg("m", "method", "Method to solve the Bethe-Salpeter equation.", false, "diag", &allowedMethods, cmd); TCLAP::ValueArg bandsArg("b", "bands", "Computes the bands of the system on the specified kpoints.", false, "kpoints.txt", "Filename", cmd); - + TCLAP::ValueArg screeningArg("z", "screening", "Provides input parameters for computing the screening.", false, "model.screening", "Filename", cmd); TCLAP::UnlabeledValueArg systemArg("systemfile", "System file", true, "system.txt", "filename", cmd); TCLAP::UnlabeledValueArg excitonArg("excitonfile", "Exciton file", false, "exciton.txt", "filename", cmd); - cmd.parse(argc, argv); // Extract information from parsed CLI options @@ -71,10 +70,11 @@ int main(int argc, char* argv[]){ std::string systemfile = systemArg.getValue(); std::string excitonfile = excitonArg.getValue(); std::string kpointsfile = bandsArg.getValue(); - + std::string screeningfile = screeningArg.getValue(); // Init. configurations std::unique_ptr systemConfig; std::unique_ptr excitonConfig; + std::unique_ptr screeningConfig; if (dftArg.isSet()){ systemConfig.reset(new xatu::CRYSTALConfiguration(systemfile, ncells)); @@ -104,13 +104,18 @@ int main(int argc, char* argv[]){ system.solveBands(kpointsfile); return 0; - } - else{ + } else if (screeningArg.isSet() && !excitonArg.isSet()){ + throw std::invalid_argument("For screening, both screening and exciton files must be provided."); + } else if (!screeningArg.isSet() && excitonArg.isSet()) { if (!excitonArg.isSet()){ throw std::invalid_argument("Must provide exciton file."); } excitonConfig.reset(new xatu::ExcitonConfiguration(excitonfile)); + + } else { + screeningConfig.reset(new xatu::ScreeningConfiguration(screeningfile)); + excitonConfig.reset(new xatu::ExcitonConfiguration(excitonfile)); } // -------------------------- Main body --------------------------- @@ -120,13 +125,25 @@ int main(int argc, char* argv[]){ cout << "+---------------------------------------------------------------------------+" << endl; cout << "| Parameters |" << endl; cout << "+---------------------------------------------------------------------------+" << endl; - + xatu::ExcitonTB bulkExciton = xatu::ExcitonTB(*systemConfig, *excitonConfig); bulkExciton.setMode(excitonConfig->excitonInfo.mode); bulkExciton.system->setAU(dftArg.isSet()); + if (screeningArg.isSet()){ + bulkExciton.initializeScreeningAttributes(*screeningConfig,excitonConfig->excitonInfo.mode); + } + + bulkExciton.verifypotential(); + cout << std::left << std::setw(30) << "System configuration file: " << std::setw(10) << systemfile << endl; - cout << std::left << std::setw(30) << "Exciton configuration file: " << std::setw(10) << excitonfile << "\n" << endl; + cout << std::left << std::setw(30) << "Exciton configuration file: " << std::setw(10) << excitonfile << endl; + if (screeningArg.isSet()){ + cout << std::left << std::setw(30) << "Screening configuration file: " << std::setw(10) << screeningfile << "\n" << endl; + } else { + cout << std::left << std::setw(30) << "Screening configuration file: " << std::setw(10) << "Not provided.\n" << endl; + } + bulkExciton.printInformation(); cout << "+---------------------------------------------------------------------------+" << endl; @@ -143,8 +160,59 @@ int main(int argc, char* argv[]){ if(!excitonConfig->excitonInfo.shift.is_empty()){ bulkExciton.system->shiftBZ(excitonConfig->excitonInfo.shift); } - + + bulkExciton.initializeHamiltonian(); + + // If screening flag is present, computes the static dielectric function first + if(screeningArg.isSet()){ + + if (screeningConfig->screeningInfo.function == "dielectric") { + + std::complex epsilon = bulkExciton.computesingleDielectricFunctionMatrixElement(); + + return 0; + } else if (screeningConfig->screeningInfo.function == "polarizability") { + + if (bulkExciton.mode == "reciprocalspace") + { + bulkExciton.writeBZtofile(); + } + + bulkExciton.PolarizabilityMesh(); + + return 0; + + } else if (screeningConfig->screeningInfo.function == "inversedielectric") { + std::cout << "Proceeding with computation of the inverse of a dielectric matrix...\n" << std::endl; + + bulkExciton.computesingleInverseDielectricMatrix(excitonConfig->excitonInfo.label); + + return 0; + + } else if (screeningConfig->screeningInfo.function == "exciton"){ + + std::cout << "Proceeding with computation of the permittivity matrix..." << std::endl; + + if (bulkExciton.mode == "reciprocalspace") + { + bulkExciton.writeBZtofile(); + } + + bulkExciton.compute_2D_DielectricMatrix(); + + bulkExciton.invertDielectricMatrix(); + + std::string filename_dielectric = excitonConfig->excitonInfo.label; + + bulkExciton.writeInverseDielectricMatrix(filename_dielectric + "_invepsilon.dat"); + + } else { + std::cout << "\nThe value '" + screeningConfig->screeningInfo.function + "' assigned to 'function' not recognized. Terminating program.\n" << std::endl; + return 0; + } + } + bulkExciton.BShamiltonian(); auto results = bulkExciton.diagonalize(method, nstates); diff --git a/src/ConfigurationBase.cpp b/src/ConfigurationBase.cpp index 14a74eb..ee22b41 100755 --- a/src/ConfigurationBase.cpp +++ b/src/ConfigurationBase.cpp @@ -28,7 +28,7 @@ ConfigurationBase::ConfigurationBase(std::string file) : filename(file){ m_file.open(file.c_str()); if(!m_file.is_open()){ - throw std::invalid_argument("ConfigurationBase: file does not exist"); + throw std::invalid_argument("ConfigurationBase: file '" + file + "' does not exist"); } }; diff --git a/src/ExcitonConfiguration.cpp b/src/ExcitonConfiguration.cpp index 7a37951..d5732dd 100755 --- a/src/ExcitonConfiguration.cpp +++ b/src/ExcitonConfiguration.cpp @@ -79,9 +79,10 @@ void ExcitonConfiguration::parseContent(){ std::vector eps = parseLine(content[0]); excitonInfo.eps = arma::vec(eps); } - else if(arg == "reciprocal"){ + else if(arg == "gcutoff"){ excitonInfo.mode = "reciprocalspace"; - excitonInfo.nReciprocalVectors = parseScalar(content[0]); + excitonInfo.Gc_ReciprocalVectors = parseScalar(content[0]); + excitonInfo.Gcutoff_found = true; } else if(arg == "exchange"){ std::string str = parseWord(content[0]); @@ -107,6 +108,9 @@ void ExcitonConfiguration::parseContent(){ else if(arg == "regularization"){ excitonInfo.regularization = parseScalar(content[0]); } + else if(arg == "percentage"){ + excitonInfo.percentage = parseScalar(content[0]); + } else{ std::cout << "Unexpected argument: " << arg << ", skipping block..." << std::endl; } @@ -145,14 +149,17 @@ void ExcitonConfiguration::checkContentCoherence(){ } } if (!potentialFound){ - throw std::invalid_argument("Specified 'potential' not supported. Use 'keldysh' or 'coulomb'"); + throw std::invalid_argument("Specified 'potential' not supported. Use 'keldysh', 'coulomb' or 'rpa'"); } if (excitonInfo.exchange && !exchangePotentialFound){ - throw std::invalid_argument("Specified 'exchange.potential' not supported. Use 'keldysh' or 'coulomb'"); + throw std::invalid_argument("Specified 'exchange.potential' not supported. Use 'keldysh', 'coulomb' or 'rpa'"); } if (excitonInfo.mode != "realspace" && excitonInfo.mode != "reciprocalspace"){ throw std::invalid_argument("Invalid mode. Use 'realspace' or 'reciprocalspace'"); } + if (excitonInfo.Gc_ReciprocalVectors < 0){ + throw std::invalid_argument("Gcutoff must be a positive number"); + } }; } \ No newline at end of file diff --git a/src/ExcitonTB.cpp b/src/ExcitonTB.cpp index db64500..45a7ace 100644 --- a/src/ExcitonTB.cpp +++ b/src/ExcitonTB.cpp @@ -1,12 +1,37 @@ #include #include +#include #include "xatu/ExcitonTB.hpp" #include "xatu/utils.hpp" #include "xatu/davidson.hpp" - +#include using namespace arma; using namespace std::chrono; +/** + *Method to prompt user to continue + *@param message + *@return void +*/ +void continueprompt(std::string message){ + + std::string to_continue = "_"; + + while(to_continue != "y" && to_continue != "n"){ + std::cout << message; + std::getline(std::cin, to_continue); + if (to_continue == "n"){ + std::cout << "You have chosen not to continue. Exiting.\n"; + exit(1); + } else if (to_continue == "y") { + continue; + } else { + std::cout << "Option not recognized. Please enter 'y' or 'n' (without the ticks).\n"; + continue; + } + } +} + namespace xatu { /** @@ -19,7 +44,7 @@ namespace xatu { */ void ExcitonTB::initializeExcitonAttributes(int ncell, const arma::ivec& bands, const arma::rowvec& parameters, const arma::rowvec& Q){ - this->ncell_ = ncell; + this->ncell_ = ncell; this->totalCells_ = pow(ncell, system_->ndim); this->Q_ = Q; this->bands_ = bands; @@ -39,9 +64,8 @@ void ExcitonTB::initializeExcitonAttributes(int ncell, const arma::ivec& bands, } else { this->rz_ = 0.5 * (this->r0_ + this->ry_); } - - this->cutoff_ = ncell/2.5; // Default value, seems to preserve crystal point group + this->cutoff_ = ncell/2.5; // Default value, seems to preserve crystal point group if(r0 == 0){ throw std::invalid_argument("Error: r0 must be non-zero"); } @@ -61,6 +85,12 @@ void ExcitonTB::initializeExcitonAttributes(const ExcitonConfiguration& cfg){ arma::ivec bands = cfg.excitonInfo.bands; arma::rowvec parameters = arma::conv_to::from(cfg.excitonInfo.eps); arma::rowvec Q = cfg.excitonInfo.Q; + double percentage = cfg.excitonInfo.percentage; + + if (2*nbands > system->basisdim){ + std::cout << "Error: Number of bands cannot be higher than actual material bands" << std::endl; + exit(1); + } if (bands.empty()){ bands = arma::regspace(- nbands + 1, nbands); @@ -69,7 +99,7 @@ void ExcitonTB::initializeExcitonAttributes(const ExcitonConfiguration& cfg){ initializeExcitonAttributes(ncell, bands, parameters, Q); std::vector valence, conduction; - for(int i = 0; i < bands.n_elem; i++){ + for(uint i = 0; i < bands.n_elem; i++){ if (bands(i) <= 0){ valence.push_back(bands(i) + system->fermiLevel); } @@ -85,13 +115,195 @@ void ExcitonTB::initializeExcitonAttributes(const ExcitonConfiguration& cfg){ this->exchange = cfg.excitonInfo.exchange; this->scissor_ = cfg.excitonInfo.scissor; this->mode_ = cfg.excitonInfo.mode; - this->nReciprocalVectors_ = cfg.excitonInfo.nReciprocalVectors; + this->Gc_exciton_ = cfg.excitonInfo.Gc_ReciprocalVectors; this->regularization_ = cfg.excitonInfo.regularization; if (regularization_ == 0){ regularization_ = system->a; } this->potential_ = cfg.excitonInfo.potential; this->exchangePotential_ = cfg.excitonInfo.exchangePotential; + + this->percentage_ = percentage; + + if (cfg.excitonInfo.Gcutoff_found){ + this->Gc_exciton_ = cfg.excitonInfo.Gc_ReciprocalVectors; + } else { + this->Gc_exciton_ = 3.0; + } + + if (this->mode == "reciprocalspace"){ + if (this->trunreciprocalLattice_.is_empty()){ + + this->trunreciprocalLattice_ = system_->truncateReciprocalSupercell(this->Gc_exciton_); + + this->nReciprocalVectors_ = this->trunreciprocalLattice_.n_rows; + } + } else if (this->mode == "realspace"){ + std::cout << "Doing nothing for now\n"; + } +} + +/* + * Method to verify if the chosen potential was 'rpa' while a screening file was provided or not + * @return void +*/ +void ExcitonTB::verifypotential(){ + if ((this->potential_ == "rpa" || this->exchangePotential_ == "rpa") && this->isscreeningset == false) { + std::cout << "To use the rpa potential, a screening configuration file must be provided." << std::endl; + exit(1); + } + + if ((this->potential_ != "rpa" || (this->exchangePotential_ != "rpa" && this->exchange)) && this->isscreeningset == true && this->function_ == "exciton") { + // continueprompt("You have provided a screening file, yet you have not chosen the rpa potential.\nDo you wish to continue?[y/n]\n"); + std::cout << "You have provided a screening file, yet you have not chosen the rpa potential." << std::endl; + exit(1); + } +} + +/** + * Method to set the screening attributes of an exciton object from a ScreeningConfiguration object. + * @details Overload of the method to use a configuration object. Based on the parametric method. + * @param cfg ScreeningConfiguration object from parsed file. + * @return void + */ +void ExcitonTB::initializeScreeningAttributes(const ScreeningConfiguration& cfg){ + uint nvalencebands = cfg.screeningInfo.nvbands; + uint nconductionbands = cfg.screeningInfo.ncbands; + arma::rowvec q = cfg.screeningInfo.q; + arma::ivec gs = cfg.screeningInfo.Gs; + std::string function = cfg.screeningInfo.function; + uint ncell_aux = cfg.screeningInfo.ncell_aux; + bool model_has_spin = cfg.screeningInfo.spin; + bool isotropic = cfg.screeningInfo.isotropic; + double Gcutoff = cfg.screeningInfo.Gcutoff; + double d = cfg.screeningInfo.d; + + this->isscreeningset = true; + this->function_ = function; + this->ncell_aux_ = ncell_aux; + this->nk_aux_ = pow(ncell_aux, 2); + this->Gcutoff_ = Gcutoff; + this->isotropic = isotropic; + this->d_ = d; + + uint totalvbands = system->fermiLevel + 1; + uint totalcbands = system->basisdim - totalvbands; + + if (nvalencebands > totalvbands || nconductionbands > totalcbands){ + std::cout << "Number of included bands cannot be higher than the number of material bands" << std::endl; + std::cout << "Number of total valence bands = " << totalvbands<< std::endl; + std::cout << "Number of total conduction bands = " << totalcbands << std::endl; + + exit(1); + } + + if (nvalencebands + nconductionbands > (uint)system->basisdim){ + std::cout << "Error: Number of bands cannot be higher than actual material" << std::endl; + std::cout << "Total number of bands is " << system->basisdim << std::endl; + exit(1); + } + + this->q_ = q; + + this->nvalencebands_ = nvalencebands; + this->nconductionbands_ = nconductionbands; + + this->Gs_ = gs; + + if (model_has_spin) { + this->g_s = 1; + } else { + this->g_s = 2; + } + + std::vector valence, conduction; + int basisdim = system->basisdim; + + for(int i = 0; i < basisdim; i++){ + if (i <= system->fermiLevel){ + valence.push_back(i); + } + else{ + conduction.push_back(i); + } + } + + this->valencebands_ = arma::ivec(valence); + this->conductionbands_ = arma::ivec(conduction); + + std::cout << "Creating the coarser BZ mesh... " << std::flush; + + int ndim = 2; + arma::mat kpoints(pow(ncell_aux, ndim), 3); + arma::mat combinations = system->generateCombinations(ncell_aux, ndim); + if (ncell_aux % 2 == 1) + { + combinations += 1. / 2; + } + + for (uint i = 0; i < nk_aux; i++) + { + arma::rowvec kpoint = arma::zeros(3); + for (int j = 0; j < ndim; j++) + { + kpoint += (2 * combinations.row(i)(j) - ncell_aux) / (2 * ncell_aux) * system->reciprocalLattice_.row(j); + } + kpoints.row(i) = kpoint; + } + + this->kpoints_aux_ = kpoints; + this->nk_aux_ = kpoints.n_rows; + + std::cout << "Done. Number of k points in the coarser BZ mesh: " << nk_aux << "\n" << std::endl; + + this->eigveckStack_ = arma::cx_cube(basisdim, basisdim, nk_aux); // For the dielectric function + this->eigvalkStack_ = arma::mat(basisdim, nk_aux); + + if (this->mode == "realspace"){ + if (cfg.screeningInfo.function == "exciton"){ + std::cout << "Numerical screening in real space not implemented." << std::endl; + } + } else if (this->mode == "reciprocalspace"){ + double radius = this->Gcutoff_; + this->trunreciprocalLattice_ = system_->truncateReciprocalSupercell(radius); + + uint ngs = this->nGs = this->trunreciprocalLattice_.n_rows; + + if (ngs < (uint) this->nReciprocalVectors) { + std::cout << "Warning: Number of reciprocal lattice vectors for the screening (" + std::to_string(ngs) + ") may not be less than the number of vectors included for the exciton (" + std::to_string(this->nReciprocalVectors_) + "). Defaulting the exciton G cutoff to the screening G cutoff.\n" << std::endl; + this->Gc_exciton_ = this->Gcutoff_; + this->nReciprocalVectors_ = ngs; + } + + if (cfg.screeningInfo.function == "dielectric" || cfg.screeningInfo.function == "polarizability"){ + if (gs(0) >= ngs || gs(1) >= ngs){ + std::cout << "Error: Index of the reciprocal vector must not be higher than number of reciprocal vectors" << std::endl; + std::cout << "Number of reciprocal vectors is " << ngs << std::endl; + + exit(1); + } + } + + if (cfg.screeningInfo.function == "exciton"){ + int nks = this->ncell*this->ncell; + this->Chimatrix_ = arma::cx_cube(ngs, ngs, nks, arma::fill::zeros); + this->epsilonmatrix_ = arma::cx_cube(ngs, ngs, nks, arma::fill::zeros); + this->Invepsilonmatrix_ = arma::cx_cube(ngs, ngs, nks, arma::fill::zeros); + } + } +} + +/** + * Method to set the screening attributes of an exciton object from a ScreeningConfiguration object and the mode specified. + * @details Overload of the method to use a configuration object. Based on the parametric method. + * @param cfg ScreeningConfiguration object from parsed file. + * @param mode Real space or reciprocal space mode + * @return void + */ +void ExcitonTB::initializeScreeningAttributes(const ScreeningConfiguration& cfg, const std::string mode){ + + this->initializeScreeningAttributes(cfg); + this->setMode(mode); } /** @@ -111,13 +323,13 @@ ExcitonTB::ExcitonTB(const SystemConfiguration& config, int ncell, const arma::i initializeExcitonAttributes(ncell, bands, parameters, Q); if (bands.n_elem > excitonbasisdim){ - cout << "Error: Number of bands cannot be higher than actual material bands" << endl; + std::cout << "Error: Number of bands cannot be higher than actual material bands" << endl; exit(1); } // arma::ivec is implemented with typedef s64 std::vector valence, conduction; - for(int i = 0; i < bands.n_elem; i++){ + for(uint i = 0; i < bands.n_elem; i++){ if (bands(i) <= 0){ valence.push_back(bands(i) + system->fermiLevel); } @@ -130,6 +342,7 @@ ExcitonTB::ExcitonTB(const SystemConfiguration& config, int ncell, const arma::i this->bandList_ = arma::conv_to::from(arma::join_cols(valenceBands, conductionBands)); }; + /** * Exciton constructor from a SystemConfiguration object. One specifies the number of valence and conduction * bands, as well as the other parameters. @@ -145,7 +358,7 @@ ExcitonTB::ExcitonTB(const SystemConfiguration& config, int ncell, int nbands, i ExcitonTB(config, ncell, {}, parameters, Q){ if (2*nbands > system->basisdim){ - cout << "Error: Number of bands cannot be higher than actual material bands" << endl; + std::cout << "Error: Number of bands cannot be higher than actual material bands" << endl; exit(1); } @@ -158,6 +371,79 @@ ExcitonTB::ExcitonTB(const SystemConfiguration& config, int ncell, int nbands, i this->bandList_ = arma::conv_to::from(arma::join_cols(valenceBands, conductionBands)); }; +/** + * Exciton constructor from a SystemConfiguration object and a vector with the bands that form + * the exciton, as well as the other parameters. + * @param config SystemConfiguration object from config file. + * @param ncell Number of unit cells along each axis. + * @param bands Vector with the indices of the bands that form the exciton. + * @param parameters Vector with dielectric constants and screening length. + * @param Q Center-of-mass momentum. + */ +ExcitonTB::ExcitonTB(const SystemConfiguration& config, int ncell, int nbands, int nrmbands, + const arma::rowvec& parameters, const arma::rowvec& Q, const uint ncell_aux, const uint nvbands, const uint ncbands, const double Gcutoff, const double Gc_exciton, const double d, const bool spin, const bool isotropic) : ExcitonTB(config, ncell, {}, parameters, Q) +{ + if (2 * nbands > system->basisdim) + { + std::cout << "Error: Number of bands cannot be higher than actual material bands" << endl; + exit(1); + } + + int fermiLevel = system->fermiLevel; + this->valenceBands_ = arma::regspace(fermiLevel - nbands - nrmbands + 1, + fermiLevel - nrmbands); + this->conductionBands_ = arma::regspace(fermiLevel + 1 + nrmbands, + fermiLevel + nbands + nrmbands); + this->bands_ = arma::join_cols(valenceBands, conductionBands) - fermiLevel; + this->bandList_ = arma::conv_to::from(arma::join_cols(valenceBands, conductionBands)); + this->Gcutoff_ = Gcutoff; + this->Gc_exciton_ = Gc_exciton; + this->mode_ = "reciprocalspace"; + this->nReciprocalVectors_ = system_->truncateReciprocalSupercell(this->Gc_exciton_).n_rows; + this->trunreciprocalLattice_ = system_->truncateReciprocalSupercell(this->Gcutoff_); + this->isscreeningset = true; + + if (this->nReciprocalVectors_ > (int) this->trunreciprocalLattice_.n_rows) { + std::cout << "Warning: Number of reciprocal lattice vectors for the exciton (" + std::to_string(this->nReciprocalVectors_) + ") may not exceed the number of vectors included in the screening (" + std::to_string(this->trunreciprocalLattice_.n_rows) + "). Defaulting the exciton G cutoff to the screening G cutoff." << std::endl; + this->Gc_exciton_ = this->Gcutoff_; + } + + uint totalvbands = system->fermiLevel + 1; + uint totalcbands = (uint)system->basisdim - totalvbands; + + if (nvbands > totalvbands || ncbands > totalcbands){ + std::cout << "Number of included bands cannot be higher than the number of material bands" << std::endl; + std::cout << "Number of total valence bands = " << totalvbands<< std::endl; + std::cout << "Number of total conduction bands = " << totalcbands << std::endl; + + exit(1); + } + + if (nvbands + ncbands > (uint)system->basisdim){ + std::cout << "Error: Number of bands cannot be higher than actual material" << std::endl; + std::cout << "Total number of bands is " << system->basisdim << std::endl; + exit(1); + } + + this->nvalencebands_ = nvbands; + this->nconductionbands_ = ncbands; + + if (spin) { + this->g_s = 1; + } else { + this->g_s = 2; + } + + this->isotropic_ = isotropic; + this->d_ = d; + + uint basisdim = system_->basisdim; + this->ncell_aux_ = ncell_aux; + uint nk_aux = pow(ncell_aux, 2); + this->nk_aux_ = nk_aux; + this->eigveckStack_ = arma::cx_cube(basisdim, basisdim, nk_aux); // For the dielectric function + this->eigvalkStack_ = arma::mat(basisdim, nk_aux); +}; /** * Exciton constructor from SystemConfiguration and ExcitonConfiguration. @@ -170,6 +456,19 @@ ExcitonTB::ExcitonTB(const SystemConfiguration& config, const ExcitonConfigurati initializeExcitonAttributes(excitonConfig); } +/** + * Exciton constructor from SystemConfiguration, ScreeningConfiguration and ExcitonConfiguration. + * @param config SystemConfiguration object. + * @param excitonConfig ExcitonConfiguration object. + * @param screeningConfig ExcitonConfiguration object. + */ +ExcitonTB::ExcitonTB(const SystemConfiguration& config, const ExcitonConfiguration& excitonConfig, const ScreeningConfiguration& screeningConfig){ + + system_.reset(new SystemTB(config)); + initializeExcitonAttributes(excitonConfig); + initializeScreeningAttributes(screeningConfig, excitonConfig.excitonInfo.mode); +} + ExcitonTB::ExcitonTB(std::shared_ptr sys, int ncell, const arma::ivec& bands, const arma::rowvec& parameters, const arma::rowvec& Q){ @@ -177,14 +476,14 @@ ExcitonTB::ExcitonTB(std::shared_ptr sys, int ncell, const arma::ivec& system_ = sys; initializeExcitonAttributes(ncell, bands, parameters, Q); - if (bands.n_elem > system->basisdim){ - cout << "Error: Number of bands cannot be higher than actual material bands" << endl; + if ((int) bands.n_elem > system->basisdim){ + std::cout << "Error: Number of bands cannot be higher than actual material bands" << std::endl; exit(1); } // arma::ivec is implemented with typedef s64 std::vector valence, conduction; - for(int i = 0; i < bands.n_elem; i++){ + for(uint i = 0; i < bands.n_elem; i++){ if (bands(i) <= 0){ valence.push_back(bands(i) + system->fermiLevel); } @@ -211,7 +510,7 @@ ExcitonTB::ExcitonTB(std::shared_ptr sys, int ncell, int nbands, int n ExcitonTB(sys, ncell, {}, parameters, Q) { if (2*nbands > system->basisdim){ - cout << "Error: Number of bands cannot be higher than actual material bands" << endl; + std::cout << "Error: Number of bands cannot be higher than actual material bands" << endl; exit(1); } @@ -304,6 +603,30 @@ void ExcitonTB::setGauge(std::string gauge){ this->gauge_ = gauge; } +/** + * Sets the number of valence bands included in the computation of the screening. + * @param nvbands + * @return void + */ +void ExcitonTB::setValenceBands(int nvbands){ + if(nvbands <= 0){ + throw std::invalid_argument("setValenceBands(): number of valence bands must be a positive integer"); + } + this->nvalencebands_ = nvbands; +} + +/** + * Sets the number of conduction bands included in the computation of the screening. + * @param ncbands + * @return void + */ +void ExcitonTB::setConductionBands(int ncbands){ + if(ncbands <= 0){ + throw std::invalid_argument("setConductionBands(): number of valence bands must be a positive integer"); + } + this->nconductionbands_ = ncbands; +} + /** * Sets the type of calculation used to obtain the exciton spectrum. It can be 'realspace' (default) * or 'reciprocalspace'. @@ -314,19 +637,12 @@ void ExcitonTB::setMode(std::string mode){ if(mode != "realspace" && mode != "reciprocalspace"){ throw std::invalid_argument("setMode(): mode must be either realspace or reciprocalspace"); } - this->mode_ = mode; -} -/** - * Sets the number of reciprocal vectors to use if the exciton calculation is set to 'reciprocalspace'. - * @param nReciprocalVector Number of reciprocal vectors to sum over. - * @return void - */ -void ExcitonTB::setReciprocalVectors(int nReciprocalVectors){ - if(nReciprocalVectors < 0){ - throw std::invalid_argument("setReciprocalVectors(): given number must be positive"); + if (mode == "reciprocalspace" && this->trunreciprocalLattice_.is_empty()) { + this->trunreciprocalLattice_ = this->system->truncateReciprocalSupercell(this->Gcutoff_); } - this->nReciprocalVectors_ = nReciprocalVectors; + + this->mode_ = mode; } /** @@ -338,136 +654,450 @@ void ExcitonTB::setRegularization(double regularization){ this->regularization_ = regularization; } -/*---------------------------------------- Potentials ----------------------------------------*/ - -/** - * Purpose: Compute Struve function H0(x). - * Source: http://jean-pierre.moreau.pagesperso-orange.fr/Cplus/mstvh0_cpp.txt - * @param X x --- Argument of H0(x) ( x ò 0 ) - * @param SH0 SH0 --- H0(x). The return value is written to the direction of the pointer. +/** + * Sets the cutoff in length for truncation of the reciprocal lattice. + * @param Gcutoff Cutoof in Angstroms^-1. + * @return void */ -void ExcitonTB::STVH0(double X, double *SH0) { - double A0,BY0,P0,Q0,R,S,T,T2,TA0; - int K, KM; - - S=1.0; - R=1.0; - if (X <= 20.0) { - A0=2.0*X/PI; - for (K=1; K<61; K++) { - R=-R*X/(2.0*K+1.0)*X/(2.0*K+1.0); - S=S+R; - if (fabs(R) < fabs(S)*1.0e-12) goto e15; - } - e15: *SH0=A0*S; - } - else { - KM=int(0.5*(X+1.0)); - if (X >= 50.0) KM=25; - for (K=1; K<=KM; K++) { - R=-R*pow((2.0*K-1.0)/X,2); - S=S+R; - if (fabs(R) < fabs(S)*1.0e-12) goto e25; - } - e25: T=4.0/X; - T2=T*T; - P0=((((-.37043e-5*T2+.173565e-4)*T2-.487613e-4)*T2+.17343e-3)*T2-0.1753062e-2)*T2+.3989422793; - Q0=T*(((((.32312e-5*T2-0.142078e-4)*T2+0.342468e-4)*T2-0.869791e-4)*T2+0.4564324e-3)*T2-0.0124669441); - TA0=X-0.25*PI; - BY0=2.0/sqrt(X)*(P0*sin(TA0)+Q0*cos(TA0)); - *SH0=2.0/(PI*X)*S+BY0; - } -} +void ExcitonTB::setGcutoff(double Gcutoff){ + if(Gcutoff < 0){ + throw std::invalid_argument("setGcutoff(): G cutoff for the screening must be positive"); + } + uint nGs_aux = this->trunreciprocalLattice_.n_rows; + arma::mat reciprocalLattice_old = this->trunreciprocalLattice_; -/** - * Calculate value of interaction potential (Keldysh). Units are eV. - * @details If the distance is zero, then the interaction is renormalized to be V(a) since - * V(0) is infinite, where a is the lattice parameter. Also, for r > cutoff the interaction is taken to be zero. - * @param r Distance at which we evaluate the potential. - * @return Value of Keldysh potential, V(r). - */ -double ExcitonTB::keldysh(arma::rowvec r){ - double eps_bar = (eps_m + eps_s)/2; - double SH0; - double cutoff = arma::norm(system->bravaisLattice.row(0)) * cutoff_ + 1E-5; - arma::rowvec R0 = {r0,ry,rz}; - double R = arma::norm(r/R0); - double r_norm = arma::norm(r); - double r0avg = (r0 + ry + rz)/3; - double potential_value; - if(r_norm < 1E-10){ - STVH0(regularization/r0, &SH0); - potential_value = ec/(8E-10*eps0*eps_bar*r0avg)*(SH0 - y0(regularization/r0avg)); + if (Gcutoff != this->Gcutoff_) { + this->trunreciprocalLattice_ = this->system->truncateReciprocalSupercell(Gcutoff); // Reset the truncated reciprocal lattice if Gcutoff changes } - else if (r_norm > cutoff){ - potential_value = 0.0; + + this->Gcutoff_ = Gcutoff; + uint nGs = this->trunreciprocalLattice_.n_rows; + this->nGs = nGs; + this->Gc_exciton_ = Gcutoff; + this->nReciprocalVectors_ = nGs; + if (nGs_aux < nGs) { + this->trunreciprocalLattice_.submat(0, 0, nGs_aux - 1, 2) = reciprocalLattice_old; // When increasing the G cutoff, conserves the order of the G vectors } - else{ - STVH0(R, &SH0); - potential_value = ec/(8E-10*eps0*eps_bar*r0avg)*(SH0 - y0(R)); - }; - return potential_value; -}; + std::cout << "Updated reciprocal lattice:" << std::endl; + printReciprocalLattice(); +} /** - * Coulomb potential in real space. - * @param r Distance at which we evaluate the potential. - * @param regularization Regularization distance to remove divergence at r=0. - * @return Value of Coulomb potential, V(r). - */ -double ExcitonTB::coulomb(arma::rowvec r){ - double cutoff = arma::norm(system->bravaisLattice.row(0)) * cutoff_ + 1E-5; - double R = abs(arma::norm(r)); - if (R > cutoff){ - return 0.0; + * Sets the vectors of the real/reciprocal lattice, where the polarizability will be computed at. + * @details Receives as argument an arma::ivec object. + * @param indeces_vec Vector containing the two indices. + * @return void +*/ +void ExcitonTB::setVectors(arma::ivec indeces_vec){ + if(indeces_vec(0) < 0 || indeces_vec(1) < 0){ + throw std::invalid_argument("setVectors(arma::ivec): Both vectors must have a positive index"); } - return (R != 0) ? ec/(4E-10*PI*eps0*R) : ec*1E10/(4*PI*eps0*regularization); + this->Gs_ = indeces_vec; } /** - * Method to select the potential to be used in the of the exciton calculation. - * @param potential Potential to be used in the direct term. - * @return Pointer to function representing the potential. - */ - -potptr ExcitonTB::selectPotential(std::string potential){ - if(potential == "keldysh"){ - return &ExcitonTB::keldysh; - } - else if(potential == "coulomb"){ - return &ExcitonTB::coulomb; - } - else{ - throw std::invalid_argument("selectPotential(): potential must be either 'keldysh' or 'coulomb'"); + * Sets the vectors of the real/reciprocal lattice, where the polarizability will be computed at. + * @param index1 Index of the first vector. + * @param index2 Index of the second vector. + * @return void +*/ +void ExcitonTB::setVectors(int index1, int index2){ + if(index1 < 0 || index2 < 0){ + throw std::invalid_argument("setVectors(int,int): Both vectors must have a positive index"); } + setVectors(arma::ivec({index1, index2})); } +/** + * Sets the potential for the direct interaction matrix elements. + * @param potential Type of potential to be used. + * @return void + */ +void ExcitonTB::setPotential(std::string potential){ + if(potential != "keldysh" && potential != "coulomb" && potential != "rpa"){ + throw std::invalid_argument("setPotential(): potential must be either keldysh, coulomb or rpa"); + } - -/*---------------------------------------- Fourier transforms ----------------------------------------*/ + this->potential_ = potential; +} + +/** + * Sets the exchange potential for the exchange interaction matrix elements. + * @param potential Type of potential to be used. + * @return void + */ +void ExcitonTB::setExchangePotential(std::string potential){ + if(potential != "keldysh" && potential != "coulomb" && potential != "rpa"){ + throw std::invalid_argument("setExchangePotential(): potential must be either keldysh, coulomb or rpa"); + } + + this->exchangePotential_ = potential; +} + +/** + * Sets the truncated lattice with given number of cells and cutoff as input. + * @param ncell Number of cells + * @param cutoff Cutoff + * @return void + */ +void ExcitonTB::setTrunLattice(int ncell, double cutoff){ + double radius = arma::norm(system->bravaisLattice.row(0)) * cutoff; + this->trunLattice_ = system->truncateSupercell(ncell, radius); +}; + +/** + * Sets the matrix that stores the q points at which we compute the dielectric matrix. + * @param q_points Matrix storing the q points. + * @return void + */ +void ExcitonTB::setq_points_list(arma::mat q_points) +{ + if (this->qpoints_list_.is_empty()) { + this->qpoints_list_.set_size(q_points.n_rows, q_points.n_cols); + } + + this->qpoints_list_ = q_points; +} + +/** + * Sets the percentage for regularization radius q0 for reciprocal space calculation of the exciton + * @param percentage + * @return void +*/ +void ExcitonTB::setPercentage(double percentage){ + this->percentage_ = percentage; +} + +/** + * Sets the thickness of the 2D system + * @param d Thickness + * @return void +*/ +void ExcitonTB::setThickness(double d){ + this->d_ = d; +} + +/* ------------------------------ Getters ------------------------------ */ +int ExcitonTB::getNGs() const { + + if (this->trunreciprocalLattice_.is_empty()){ + std::cout << "Matrix of reciprocal lattice vectors is empty. Will return 0.\n" << std::endl; + return 0; + } + + return this->trunreciprocalLattice_.n_rows; +} + +/** + * Gets the thickness of the 2D system + * @return Thickness + */ +double ExcitonTB::getThickness() const { + return this->d_; +} + +arma::cx_cube ExcitonTB::getChiMatrix() const { + + uint nks_expected = this->ncell_ * this->ncell_; + uint nks_matrix = this->Invepsilonmatrix_.n_slices; + + if(nks_expected != nks_matrix){ + std::cout << "Warning: Number of k points for the polarizability matrix (" << nks_matrix << ") does not match the size of the BZ (" << nks_expected << ")." << std::endl; + } + + return this->Chimatrix_; +} + +std::vector>>> ExcitonTB::getPolarizabilityMatrix_as_vector() const { + + uint nqs = 0; + uint nks_matrix = 0; + uint ngs = 0; + + if (this->Chimatrix_.is_empty()) { + std::cout << "Polarizability matrix is empty. Returning empty vector." << std::endl; + return std::vector>>>(); + } else { + nks_matrix = this->Chimatrix_.n_slices; + ngs = this->Chimatrix_.slice(0).n_rows; + } + + if (this->qpoints_list_.is_empty()) { + std::cout << "Warning: List of q points is not defined. Polarizability matrix will still be returned." << std::endl; + } else { + nqs = this->qpoints_list_.n_rows; + for (uint iq = 0; iq < nqs; iq++) { + arma::rowvec q_point = this->qpoints_list_.row(iq); + arma::rowvec k_point = system->meshBZ.row(iq); + if (arma::norm(q_point - k_point) > 1e-6) { + std::cout << "Warning: List of q points does not coincide with the BZ mesh. Polarizability matrix will still be returned." << std::endl; + break; + } + } + } + + std::vector>> null_matrix = std::vector>>(ngs, std::vector>(ngs, std::complex(0.0, 0.0))); + + std::vector>>> Chimatrix_as_vector; + Chimatrix_as_vector.resize(nks_matrix); + + for (uint ik = 0; ik < nks_matrix; ik++) { + arma::cx_mat inv_epsilon_at_ik = this->Chimatrix_.slice(ik); + Chimatrix_as_vector[ik].resize(ngs); + Chimatrix_as_vector[ik] = arma::conv_to>>>::from(inv_epsilon_at_ik); + } + + return Chimatrix_as_vector; +} + +arma::cx_cube ExcitonTB::getInverseDielectricMatrix() const { + + uint nks_expected = this->ncell_ * this->ncell_; + uint nks_matrix = this->Invepsilonmatrix_.n_slices; + + if(nks_expected != nks_matrix){ + std::cout << "Warning: Number of k points for the inverse dielectric matrix (" << nks_matrix << ") does not match the size of the BZ (" << nks_expected << ")." << std::endl; + } + + return this->Invepsilonmatrix_; +} + +std::vector>>> ExcitonTB::getInverseDielectricMatrix_as_vector() const { + + uint nqs = 0; + uint nks_matrix = 0; + uint ngs = 0; + + if (this->Invepsilonmatrix_.is_empty()) { + std::cout << "Inverse dielectric matrix is empty. Returning empty vector." << std::endl; + return std::vector>>>(); + } else { + nks_matrix = this->Invepsilonmatrix_.n_slices; + ngs = this->Invepsilonmatrix_.slice(0).n_rows; + } + + if (this->qpoints_list_.is_empty()) { + std::cout << "Warning: List of q points is not defined. Inverse dielectric matrix will still be returned." << std::endl; + } else { + nqs = this->qpoints_list_.n_rows; + for (uint iq = 0; iq < nqs; iq++) { + arma::rowvec q_point = this->qpoints_list_.row(iq); + arma::rowvec k_point = system->meshBZ.row(iq); + if (arma::norm(q_point - k_point) > 1e-6) { + std::cout << "Warning: List of q points does not coincide with the BZ mesh. Inverse dielectric matrix will still be returned." << std::endl; + break; + } + } + } + + std::vector>>> Invepsilonmatrix_as_vector; + Invepsilonmatrix_as_vector.resize(nks_matrix); + + for (uint ik = 0; ik < nks_matrix; ik++) { + arma::cx_mat inv_epsilon_at_ik = this->Invepsilonmatrix_.slice(ik); + Invepsilonmatrix_as_vector[ik].resize(ngs); + Invepsilonmatrix_as_vector[ik] = arma::conv_to>>>::from(inv_epsilon_at_ik); + } + + return Invepsilonmatrix_as_vector; +} + +/*---------------------------------------- Potentials ----------------------------------------*/ + +/** + * Purpose: Compute Struve function H0(x). + * Source: http://jean-pierre.moreau.pagesperso-orange.fr/Cplus/mstvh0_cpp.txt + * @param X x --- Argument of H0(x) ( x ò 0 ) + * @param SH0 SH0 --- H0(x). The return value is written to the direction of the pointer. +*/ +void ExcitonTB::STVH0(double X, double *SH0) { + double A0,BY0,P0,Q0,R,S,T,T2,TA0; + int K, KM; + + S=1.0; + R=1.0; + if (X <= 20.0) { + A0=2.0*X/PI; + for (K=1; K<61; K++) { + R=-R*X/(2.0*K+1.0)*X/(2.0*K+1.0); + S=S+R; + if (fabs(R) < fabs(S)*1.0e-12) goto e15; + } + e15: *SH0=A0*S; + } + else { + KM=int(0.5*(X+1.0)); + if (X >= 50.0) KM=25; + for (K=1; K<=KM; K++) { + R=-R*pow((2.0*K-1.0)/X,2); + S=S+R; + if (fabs(R) < fabs(S)*1.0e-12) goto e25; + } + e25: T=4.0/X; + T2=T*T; + P0=((((-.37043e-5*T2+.173565e-4)*T2-.487613e-4)*T2+.17343e-3)*T2-0.1753062e-2)*T2+.3989422793; + Q0=T*(((((.32312e-5*T2-0.142078e-4)*T2+0.342468e-4)*T2-0.869791e-4)*T2+0.4564324e-3)*T2-0.0124669441); + TA0=X-0.25*PI; + BY0=2.0/sqrt(X)*(P0*sin(TA0)+Q0*cos(TA0)); + *SH0=2.0/(PI*X)*S+BY0; + } +} + +/** + * Calculate value of interaction potential (Keldysh). Units are eV. + * @details If the distance is zero, then the interaction is renormalized to be V(a) since + * V(0) is infinite, where a is the lattice parameter. Also, for r > cutoff the interaction is taken to be zero. + * @param r Distance at which we evaluate the potential. + * @return Value of Keldysh potential, V(r). + */ +double ExcitonTB::keldysh(arma::rowvec r){ + double eps_bar = (eps_m + eps_s)/2; + double SH0; + double cutoff = arma::norm(system->bravaisLattice.row(0)) * cutoff_ + 1E-5; + arma::rowvec R0 = {r0,ry,rz}; + double R = arma::norm(r/R0); + double r_norm = arma::norm(r); + double r0avg = (r0 + ry + rz)/3; + double potential_value; + if(r_norm < 1E-10){ + STVH0(regularization/r0, &SH0); + potential_value = ec/(8E-10*eps0*eps_bar*r0avg)*(SH0 - y0(regularization/r0avg)); + } + else if (r_norm > cutoff){ + potential_value = 0.0; + } + else{ + STVH0(R, &SH0); + potential_value = ec/(8E-10*eps0*eps_bar*r0avg)*(SH0 - y0(R)); + }; + + return potential_value; +}; + +/** + * Coulomb potential in real space. + * @param r Distance at which we evaluate the potential. + * @param regularization Regularization distance to remove divergence at r=0. + * @return Value of Coulomb potential, V(r). + */ +double ExcitonTB::coulomb(arma::rowvec r){ + double cutoff = arma::norm(system->bravaisLattice.row(0)) * cutoff_ + 1E-5; + double R = abs(arma::norm(r)); + if (R > cutoff){ + return 0.0; + } + return (R != 0) ? ec/(4E-10*PI*eps0*R) : ec*1E10/(4*PI*eps0*regularization); +} + +/** + * Method to select the potential to be used in the of the exciton calculation. + * @param potential Potential to be used in the direct term. + * @return Pointer to function representing the potential. + */ + +potptr ExcitonTB::selectPotential(std::string potential){ + if(potential == "keldysh"){ + return &ExcitonTB::keldysh; + } + else if(potential == "coulomb"){ + return &ExcitonTB::coulomb; + } + else{ + throw std::invalid_argument("selectPotential(): potential must be either 'keldysh', 'coulomb'"); + } +} + +/*---------------------------------------- Fourier transforms ----------------------------------------*/ +/** + * Evaluates the 2D Fourier transform of the Coulomb potential, which is an analytical expression. + * @param k kpoint where we evaluate the FT. + * @return 2D Fourier transform of the potential at q, FT[V](q). + */ +double ExcitonTB::coulomb_2D_FT(const arma::rowvec& k) const { + + double potential = 0; + double eps = 1E-12; //arma::norm(system->reciprocalLattice.row(0))*1E-3/totalCells; + + double knorm = arma::norm(k); + if (knorm < eps){ + potential = 0; + } + else{ + potential = 1/knorm; + } + + potential = potential*ec*1E10/(2*eps0*system->unitCellArea); + + return potential; +} /** * Evaluates the Fourier transform of the Keldysh potential, which is an analytical expression. * @param q kpoint where we evaluate the FT. * @return Fourier transform of the potential at q, FT[V](q). */ -double ExcitonTB::keldyshFT(arma::rowvec q){ - double radius = cutoff*arma::norm(system->reciprocalLattice.row(0)); +double ExcitonTB::keldyshFT(arma::rowvec q) const { + double potential = 0; double eps_bar = (eps_m + eps_s)/2; - double eps = arma::norm(system->reciprocalLattice.row(0))/totalCells; + double eps = 10E-12; double qnorm = arma::norm(q); + if (qnorm < eps){ - potential = 0; + return this->W00_at_0_; } else{ potential = 1/(qnorm*(1 + r0*qnorm)); } - potential = potential*ec*1E10/(2*eps0*eps_bar*system->unitCellArea*totalCells); + potential = potential*ec*1E10/(2*eps0*eps_bar*system->unitCellArea); + + return potential; +} + +/** + * Evaluates the RPA potential in reciprocal space. + * @param q kpoint where we evaluate the FT. + * @param g index of vector G. + * @param g2 index of vector G'. + * @return W_(G,G')(q) matrix element of the screened potential + */ +std::complex ExcitonTB::rpaFT(int g, int g2, arma::rowvec q) const { + + if (this->Invepsilonmatrix_.is_empty()){ + std::cerr << "Inverse of dielectric matrix has not been computed yet. Terminating." << std::endl; + } + + std::complex potential = 0; + double eps = 1E-12; + double qnorm = arma::norm(q); + + if (qnorm < eps && g == 0 && g2 == 0){ + potential = this->W00_at_0_; + } + else if ((qnorm < eps && g == 0 && g2 != 0) || (qnorm < eps && g != 0 && g2 == 0)) + { + potential = 0.0; + } + else + { + int iq = system->findEquivalentPointBZ(q, this->ncell_); + double vc_average = 1.0; + double d = this->d_; + + arma::rowvec G = this->trunreciprocalLattice_.row(g); + arma::rowvec G2 = this->trunreciprocalLattice_.row(g2); + + if (d > 1E-4) { + vc_average = 2*std::sqrt(std::exp(-arma::norm(q + G)*d) - 1 + d*arma::norm(q+G))*std::sqrt(std::exp(-arma::norm(q + G2)*d) - 1 + d*arma::norm(q+G2))/(arma::norm(q + G)*arma::norm(q + G2)*d*d); + } + + potential = vc_average * std::sqrt(coulomb_2D_FT(q + G)) * this->Invepsilonmatrix_.slice(iq).row(g)(g2) * std::sqrt(coulomb_2D_FT(q + G2)); + } + return potential; } @@ -489,7 +1119,7 @@ std::complex ExcitonTB::motifFourierTransform(int fAtomIndex, int sAtomI arma::rowvec firstAtom = system->motif.row(fAtomIndex).subvec(0, 2); arma::rowvec secondAtom = system->motif.row(sAtomIndex).subvec(0, 2); - for(int n = 0; n < cells.n_rows; n++){ + for(uint n = 0; n < cells.n_rows; n++){ arma::rowvec cell = cells.row(n); // double module = arma::norm(cell + firstAtom - secondAtom); arma::rowvec dist = cell + firstAtom - secondAtom; @@ -562,7 +1192,7 @@ arma::cx_mat ExcitonTB::extendMotifFT(const arma::cx_mat& motifFT){ * @param coefsK3 Third eigenstate vector. * @param coefsK4 Fourth eigenstate vector. * @param motifFT Motif Fourier transform. - * @return Interaction term. + * @return Interaction term. */ std::complex ExcitonTB::realSpaceInteractionTerm(const arma::cx_vec& coefsK1, const arma::cx_vec& coefsK2, @@ -604,6 +1234,8 @@ std::complex ExcitonTB::realSpaceInteractionTerm(const arma::cx_vec& coe * @param k2 kpoint corresponding to k'. * @param kQ kpoint corresponding to k + Q. * @param k2Q kpoint corresponding to k' + Q. + * @param potential Potential used to compute the matrix element (Coulomb, Keldysh or dielectric function within RPA) + * @param nGs Number of reciprocal vectors included in the sum over G (and G') * @return Interaction term. */ std::complex ExcitonTB::reciprocalInteractionTerm(const arma::cx_vec& coefsK, @@ -614,24 +1246,68 @@ std::complex ExcitonTB::reciprocalInteractionTerm(const arma::cx_vec& co const arma::rowvec& k2, const arma::rowvec& kQ, const arma::rowvec& k2Q, - int nrcells){ - + std::string potential, + int nGs) { std::complex Ic, Iv; std::complex term = 0; - double radius = cutoff * arma::norm(system->reciprocalLattice.row(0)); - arma::mat reciprocalVectors = system_->truncateReciprocalSupercell(nrcells, radius); + arma::mat reciprocalVectors = this->trunreciprocalLattice_; - for(int i = 0; i < reciprocalVectors.n_rows; i++){ - auto G = reciprocalVectors.row(i); + arma::rowvec null_vector(3,arma::fill::zeros); - Ic = blochCoherenceFactor(coefsKQ, coefsK2Q, kQ, k2Q, G); - Iv = blochCoherenceFactor(coefsK, coefsK2, k, k2, G); + arma::rowvec k_dif = k - k2; + arma::rowvec kQ_dif = kQ - k2Q; - // must change this to include Q2DRK... - term += Ic*conj(Iv)*keldyshFT(k - k2 + G); + int k_eff_index = system_->findEquivalentPointBZ(k_dif, ncell); + int kQ_eff_index = system_->findEquivalentPointBZ(kQ_dif, ncell); + arma::rowvec k_eff = system_->kpoints.row(k_eff_index); + arma::rowvec kQ_eff = system_->kpoints.row(kQ_eff_index); + + arma::rowvec g = k_dif - k_eff; + + // If the Gcutoff for the exciton is 0, then only G=G'=0 and G=G'=g enter in the sum, and there is no shift G->G-g and G'->G'-g in the sum, as there is no sum + if (this->Gc_exciton_ < 1E-6){ + g = null_vector; } - return term; + if (potential == "coulomb"){ + for(int ig = 0; ig < nGs; ig++){ + arma::rowvec G = reciprocalVectors.row(ig); + + Ic = blochCoherenceFactor(coefsK2Q, coefsKQ, kQ, k2Q, G); + Iv = blochCoherenceFactor(coefsK2, coefsK, k, k2, G); + + term += conj(Ic)*this->coulomb_2D_FT(k - k2 + G)*Iv; + } + } else if (potential == "keldysh"){ + for(int ig = 0; ig < nGs; ig++){ + auto G = reciprocalVectors.row(ig); + + Ic = blochCoherenceFactor(coefsK2Q, coefsKQ, kQ, k2Q, G); + Iv = blochCoherenceFactor(coefsK2, coefsK, k, k2, G); + + term += conj(Ic)*this->keldyshFT(k - k2 + G)*Iv; + } + } else if (potential == "rpa"){ + for(int ig = 0; ig < nGs; ig++){ + + auto G = reciprocalVectors.row(ig) - g; + + for(int ig2 = 0; ig2 < nGs; ig2++){ + + auto G2 = reciprocalVectors.row(ig2) - g; + + Ic = blochCoherenceFactor(coefsK2Q, coefsKQ, kQ, k2Q, G); + Iv = blochCoherenceFactor(coefsK2, coefsK, k, k2, G2); + + term += conj(Ic)*this->rpaFT(ig, ig2, k_eff)*Iv; + } + } + } else { + std::cout << "Potential not valid" << std::endl; + exit(1); + } + + return term/((std::complex)totalCells); }; /** @@ -641,7 +1317,7 @@ std::complex ExcitonTB::reciprocalInteractionTerm(const arma::cx_vec& co * @param k1 kpoint k. * @param k2 kpoint k'. * @param G Reciprocal lattice vector used to compute the coherence factor. - * @return Bloch coherence factor I evaluated at G for states |nk>, |n'k'>. + * @return Bloch coherence factor I = evaluated at G for states |nk>, |n'k'>. */ std::complex ExcitonTB::blochCoherenceFactor(const arma::cx_vec& coefs1, const arma::cx_vec& coefs2, const arma::rowvec& k1, const arma::rowvec& k2, @@ -650,6 +1326,7 @@ std::complex ExcitonTB::blochCoherenceFactor(const arma::cx_vec& coefs1, std::complex imag(0, 1); arma::cx_vec coefs = arma::conj(coefs1) % coefs2; arma::cx_vec phases = arma::ones(system->basisdim); + int index_min = 0; int index_max = -1; @@ -658,7 +1335,7 @@ std::complex ExcitonTB::blochCoherenceFactor(const arma::cx_vec& coefs1, arma::rowvec atomPosition = system->motif.row(i).subvec(0, 2); index_max += system->orbitals(species); - phases.subvec(index_min, index_max) *= exp(imag*arma::dot(k1 - k2 + G, atomPosition)); + phases.subvec(index_min, index_max) *= exp(-imag*arma::dot(k1 - k2 + G, atomPosition)); index_min = index_max + 1; } @@ -669,14 +1346,53 @@ std::complex ExcitonTB::blochCoherenceFactor(const arma::cx_vec& coefs1, } -/*------------------------------------ Electron-hole pair basis ------------------------------------*/ - /** - * Method to generate a basis which is a subset of the basis considered for the - * exciton. Its main purpose is to allow computation of Fermi golden rule between - * two specified subbasis. - * @param bands Band subset of the originally specified for the exciton. - * @return Matrix with the states corresponding to the specified subset. + * Calculation of Bloch coherence factor taking into account the material's finite thickness d + * @param coefs1 Vector of eigenstate |n,k>. + * @param coefs2 Vector of eigenstate |n',k'>. + * @param k1 kpoint k. + * @param k2 kpoint k'. + * @param G Reciprocal lattice vector used to compute the coherence factor. + * @param d 2D material thickness. + * @return Bloch coherence factor I = evaluated at G for states |nk>, |n'k'>, for finite thickness. + */ +std::complex ExcitonTB::blochCoherenceFactor(const arma::cx_vec &coefs1, const arma::cx_vec &coefs2, + const arma::rowvec &k1, const arma::rowvec &k2, + const arma::rowvec &G, const double d) const { + + std::complex imag(0, 1); + arma::cx_vec coefs = arma::conj(coefs1) % coefs2; + arma::cx_vec phases = arma::ones(system->basisdim); + + int index_min = 0; + int index_max = -1; + + for (int i = 0; i < system->natoms; i++) + { + int species = system->motif.row(i)(3); + arma::rowvec atomPosition = system->motif.row(i).subvec(0, 2); + + double extra_factor = std::sqrt(2*(1 - exp(-arma::norm(k1 - k2 + G) * d/2) * cosh(arma::norm(k1 - k2 + G) * atomPosition(2)))/(d*arma::norm(k1 - k2 + G))); + + index_max += system->orbitals(species); + phases.subvec(index_min, index_max) *= extra_factor * exp(-imag * arma::dot(k1 - k2 + G, atomPosition)); + + index_min = index_max + 1; + } + + std::complex factor = arma::dot(coefs, phases); + + return factor; +} + +/*------------------------------------ Electron-hole pair basis ------------------------------------*/ + +/** + * Method to generate a basis which is a subset of the basis considered for the + * exciton. Its main purpose is to allow computation of Fermi golden rule between + * two specified subbasis. + * @param bands Band subset of the originally specified for the exciton. + * @return Matrix with the states corresponding to the specified subset. */ arma::imat ExcitonTB::specifyBasisSubset(const arma::ivec& bands){ @@ -695,9 +1411,8 @@ arma::imat ExcitonTB::specifyBasisSubset(const arma::ivec& bands){ std::cerr << e; }; - int reducedBasisDim = system->nk*bands.n_elem; std::vector valence, conduction; - for(int i = 0; i < bands.n_elem; i++){ + for(uint i = 0; i < bands.n_elem; i++){ if (bands(i) <= 0){ valence.push_back(bands(i) + system->fermiLevel); } @@ -722,152 +1437,1989 @@ arma::cx_mat ExcitonTB::fixGlobalPhase(arma::cx_mat& coefs){ arma::cx_rowvec sums = arma::sum(coefs); std::complex imag(0, 1); - for(int j = 0; j < sums.n_elem; j++){ + for(arma::uword j = 0; j < sums.n_elem; j++){ double phase = arg(sums(j)); coefs.col(j) *= exp(-imag*phase); } - return coefs; -} + return coefs; +} + +/*------------------------------------ Initializers ------------------------------------*/ + +/** + * Method to initialize the motif Fourier transform for all possible motif combination + * at a given kpoint. + * @param i Index of kpoint. + * @param cells Matrix of unit cells over which the motif FT is computed. + * @param potential Pointer to potential function. + * @return void + */ +void ExcitonTB::initializeMotifFT(int i, const arma::mat& cells, potptr potential){ + ftMotifStack.slice(i) = motifFTMatrix(system->meshBZ.row(i), cells, potential); +} + + +/** + * Main method to compute all the relevant single-particle quantities (bands, eigenstates and fourier transforms), + * to compute the Bethe-Salpeter equation. + * @details It precomputes and saves the relevant data in the heap for later computations. + * @param triangular Boolean to specify whether the Hamiltonian matrices are triangular (default = false). + * @return void + */ +void ExcitonTB::initializeResultsH0(){ + + int nTotalBands = bandList.n_elem; + double radius = arma::norm(system->bravaisLattice.row(0)) * cutoff_; + arma::mat cells = system_->truncateSupercell(ncell, radius); + + uint nk = system->nk; + uint nk_aux = this->nk_aux; + + int natoms = system->natoms; + int basisdim = system->basisdim; + + this->eigvecKStack_ = arma::cx_cube(basisdim, nTotalBands, nk); + this->eigvecKQStack_ = arma::cx_cube(basisdim, nTotalBands, nk); + this->eigvalKStack_ = arma::mat(nTotalBands, nk); + this->eigvalKQStack_ = arma::mat(nTotalBands, nk); + this->ftMotifStack = arma::cx_cube(natoms, natoms, system->meshBZ.n_rows); + this->ftMotifQ = arma::cx_mat(natoms, natoms); + + vec auxEigVal(basisdim); + arma::cx_mat auxEigvec(basisdim, basisdim); + arma::cx_mat h; + + system_->calculateInverseReciprocalMatrix(); + std::complex imag(0, 1); + + std::cout << "Diagonalizing H0 for all k points... " << std::flush; + for (uint i = 0; i < nk; i++){ + arma::rowvec k = system->kpoints.row(i); + system->solveBands(k, auxEigVal, auxEigvec); + + auxEigvec = fixGlobalPhase(auxEigvec); + eigvalKStack_.col(i) = auxEigVal(bandList); + eigvecKStack_.slice(i) = auxEigvec.cols(bandList); + + if(arma::norm(Q) != 0){ + arma::rowvec kQ = system->kpoints.row(i) + Q; + system->solveBands(kQ, auxEigVal, auxEigvec); + + auxEigvec = fixGlobalPhase(auxEigvec); + eigvalKQStack_.col(i) = auxEigVal(bandList); + eigvecKQStack_.slice(i) = auxEigvec.cols(bandList); + } + else{ + eigvecKQStack_.slice(i) = eigvecKStack.slice(i); + eigvalKQStack_.col(i) = eigvalKStack.col(i); + }; + + }; + std::cout << "Done" << std::endl; + + if(this->mode == "realspace"){ + std::cout << "Computing lattice Fourier transform... " << std::flush; + + potptr directPotential = selectPotential(this->potential_); + #pragma omp parallel for + for (unsigned int i = 0; i < system->meshBZ.n_rows; i++){ + // BIGGEST BOTTLENECK OF THE CODE + initializeMotifFT(i, cells, directPotential); + + /* AJU 24-11-23: Progress bar does not work properly with parallel for + Fix it or remove it direcly? */ + // percent = (100 * (i + 1)) / meshBZ.n_rows ; + // if (percent >= displayNext){ + // std::cout << "\r" << "[" << std::string(percent / 5, '|') << std::string(100 / 5 - percent / 5, ' ') << "]"; + // std::cout << percent << "%"; + // std::cout.flush(); + // displayNext += step; + // } + } + std::cout << "Done\n" << std::endl; + } + + if (this->mode == "reciprocalspace" && this->isscreeningset == true){ + + if (this->kpoints_aux.is_empty()) { + std::cout << "Creating the coarser BZ mesh. " << std::flush; + + int ndim = 2; + arma::mat kpoints(pow(ncell_aux, ndim), 3); + arma::mat combinations = system->generateCombinations(ncell_aux, ndim); + if (ncell_aux % 2 == 1) + { + combinations += 1. / 2; + } + + for (uint i = 0; i < nk_aux; i++) + { + arma::rowvec kpoint = arma::zeros(3); + for (int j = 0; j < ndim; j++) + { + kpoint += (2 * combinations.row(i)(j) - ncell_aux) / (2 * ncell_aux) * system->reciprocalLattice_.row(j); + } + kpoints.row(i) = kpoint; + } + this->kpoints_aux_ = kpoints; + } + + std::cout << "Diagonalizing H0(k) for all k points in the coarser BZ mesh... " << std::flush; + + for (uint i = 0; i < nk_aux; i++){ + arma::rowvec k = this->kpoints_aux.row(i); + system->solveBands(k, auxEigVal, auxEigvec); + + auxEigvec = fixGlobalPhase(auxEigvec); + eigvalkStack_.col(i) = auxEigVal; + eigveckStack_.slice(i) = auxEigvec; + }; + std::cout << "Done" << std::endl; + } + + if(this->exchange){ + potptr exchangePotential = selectPotential(this->exchangePotential_); + this->ftMotifQ = motifFTMatrix(this->Q, cells, exchangePotential); + } +}; + +/** + * Routine to initialize the required variables to construct the Bethe-Salpeter Hamiltonian. + * @param triangular Boolean to specify whether the single-particle Hamiltonian matrices are triangular. + * @return void. + */ +void ExcitonTB::initializeHamiltonian(){ + + if(bands.empty()){ + throw std::invalid_argument("Error: Exciton object must have some bands"); + } + if(system->nk == 0){ + throw std::invalid_argument("Error: BZ mesh must be initialized first"); + } + + if (this->regularization_ < 1E-10){ + regularization_ = system->a; + } + + this->excitonbasisdim_ = system->nk*valenceBands.n_elem*conductionBands.n_elem; + this->totalCells_ = pow(ncell*system->factor, system->ndim); + + std::cout << "Initializing basis for BSE... " << std::flush; + initializeBasis(); + generateBandDictionary(); + + if (this->mode == "reciprocalspace") { + printReciprocalLattice(); + } + + initializeResultsH0(); +} + +/*------------------------------------ Static dielectric function matrix elements ------------------------------------*/ +/** + * Method to compute the (G,G') matrix element of the static polarizability at the specified momentum vector q in the input file. + * @details Writes the polarizability in the file polarizability_convergence.dat as a + * function of the number of included conduction bands. The polarizability is the purely 2D version. + * @param q Momentum vector q specified in the input file + * @return Polarizability +*/ +std::complex ExcitonTB::computesinglePolarizabilityMatrixElement(arma::rowvec &q, arma::rowvec &G, arma::rowvec& G2) +{ + std::ofstream polarfile("polarizability_convergence.dat"); + + if (!polarfile.is_open()) { // check if the file was opened successfully + std::cerr << "Error opening file\n"; + } + + uint nk = this->nk_aux; + + if (this->kpoints_aux.is_empty()) { + std::cout << "Creating the coarser BZ mesh... " << std::flush; + + int ndim = 2; + arma::mat kpoints(pow(ncell_aux, ndim), 3); + arma::mat combinations = system->generateCombinations(ncell_aux, ndim); + if (ncell_aux % 2 == 1) + { + combinations += 1. / 2; + } + + for (uint i = 0; i < nk_aux; i++) + { + arma::rowvec kpoint = arma::zeros(3); + for (int j = 0; j < ndim; j++) + { + kpoint += (2 * combinations.row(i)(j) - ncell_aux) / (2 * ncell_aux) * system->reciprocalLattice_.row(j); + } + kpoints.row(i) = kpoint; + } + this->kpoints_aux_ = kpoints; + } + arma::mat k_points = this->kpoints_aux_; + + int nvbands = system->fermiLevel + 1; + + int nvbandsincluded = this->nvalencebands_; + int ncbandsincluded = this->nconductionbands_; + + int upperindexcband = nvbands + ncbandsincluded - 1; + + std::complex g_s = this->g_s; // Spin degeneracy + + std::complex term_aux = 0.; + + std::cout << "Done \n"; + + arma::cx_vec coefskq, coefsk; + arma::cx_vec coefskq_c, coefsk_v; + + for (int ic = nvbands; ic <= upperindexcband; ic++){ + + for (int iv = nvbands - 1; iv >= nvbands - nvbandsincluded; iv--){ + + for (uint ik = 0; ik < nk; ik++){ + + arma::rowvec k = k_points.row(ik); + arma::rowvec kq = k + q; + + // Using the atomic gauge + if(gauge == "atomic"){ + coefskq = system_->latticeToAtomicGauge(eigveckqStack_.slice(ik).col(iv), kq); + coefsk = system_->latticeToAtomicGauge(eigveckStack_.slice(ik).col(ic), k); + + coefskq_c = system_->latticeToAtomicGauge(eigveckqStack_.slice(ik).col(ic), kq); + coefsk_v = system_->latticeToAtomicGauge(eigveckStack_.slice(ik).col(iv), k); + } + else{ + coefskq = eigveckqStack_.slice(ik).col(iv); + coefsk = eigveckStack_.slice(ik).col(ic); + + coefskq_c = eigveckqStack_.slice(ik).col(ic); + coefsk_v = eigveckStack_.slice(ik).col(iv); + } + + std::complex IvcG = blochCoherenceFactor(coefsk, coefskq, kq, k, G); + std::complex IvcG2 = blochCoherenceFactor(coefsk, coefskq, kq, k, G2); + + std::complex IcvG = blochCoherenceFactor(coefsk_v, coefskq_c, kq, k, G); + std::complex IcvG2 = blochCoherenceFactor(coefsk_v, coefskq_c, kq, k, G2); + + term_aux += (IvcG*std::conj(IvcG2) / (eigvalkqStack_.col(ik)(iv) - eigvalkStack_.col(ik)(ic))) - (IcvG*std::conj(IcvG2) / (eigvalkqStack_.col(ik)(ic) - eigvalkStack_.col(ik)(iv))); + } + + polarfile << nvbands - iv << " " << ic - nvbands + 1 << " " << real(g_s) * real(term_aux) / (nk) << " " << real(g_s) * imag(term_aux) / (nk) << "\n"; + } + } + + polarfile.close(); + + std::cout << "The value of the polarizability is = " << g_s*term_aux/((std::complex)nk) << std::endl; + + return g_s*term_aux/((std::complex)nk); +} + +/** + * Method to compute the (G,G') matrix element of the static 2D polarizability at the specified arbitrary momentum vector q. + * @details The purely 2D polarizability is computed + * @param G Reciprocal lattice vector G + * @param G2 Reciprocal lattice vector G2 + * @param q Momentum vector q + * @return Polarizability +*/ +inline std::complex ExcitonTB::compute_2D_PolarizabilityMatrixElement(const arma::rowvec& q, const arma::rowvec& G, const arma::rowvec& G2) { + + uint nk = this->nk_aux; + + int nvbands = system->fermiLevel + 1; + int nvbandsincluded = this->nvalencebands_; + int ncbandsincluded = this->nconductionbands_; + int upperindexcband = nvbands + ncbandsincluded - 1; + + arma::cx_vec coefskq, coefsk; + + std::complex term = 0.; + std::complex g_s = this->g_s; // Spin degeneracy + + if (this->eigveckqStack_.is_empty() && this->eigvalkqStack_.is_empty()) { + std::cout << "Bloch Hamiltonian has to be diagonalized at every k+q point before computing polarizability matrix elements. Terminating" << std::endl; + exit(0); + } + + for (int ic = nvbands; ic <= upperindexcband; ic++){ + + for (int iv = nvbands - 1; iv >= nvbands - nvbandsincluded; iv--){ + + for (uint ik = 0; ik < nk; ik++){ + + arma::rowvec k = this->kpoints_aux.row(ik); + arma::rowvec kq = k + q; + + // Using the atomic gauge + if(gauge == "atomic"){ + coefskq = system_->latticeToAtomicGauge(eigveckqStack_.slice(ik).col(iv), kq); + coefsk = system_->latticeToAtomicGauge(eigveckStack_.slice(ik).col(ic), k); + } + else{ + coefskq = eigveckqStack_.slice(ik).col(iv); + coefsk = eigveckStack_.slice(ik).col(ic); + } + + std::complex IvcG = blochCoherenceFactor(coefsk, coefskq, kq, k, G); + std::complex IvcG2 = blochCoherenceFactor(coefsk, coefskq, kq, k, G2); + + term += IvcG*std::conj(IvcG2) / (eigvalkqStack_.col(ik)(iv) - eigvalkStack_.col(ik)(ic)); + } + } + } + + return g_s*2.0*term/((std::complex)nk); // Factor of 2 from TRS +} + +/** + * Method to compute the (G,G') matrix element of the static Q2D polarizability at the specified momentum q. + * @details The Q2D polarizability computed has meaning only when multiplied by the Coulomb potential + * @param G Reciprocal lattice vector G + * @param G2 Reciprocal lattice vector G2 + * @param q Momentum vector q + * @param d Thickness of the 2D system + * @return Polarizability +*/ +inline std::complex ExcitonTB::compute_quasi2D_PolarizabilityMatrixElement(const arma::rowvec& q, const arma::rowvec& G, const arma::rowvec& G2, const double d) { + + uint nk = this->nk_aux; + + int nvbands = system->fermiLevel + 1; + + int nvbandsincluded = this->nvalencebands_; + int ncbandsincluded = this->nconductionbands_; + + int upperindexcband = nvbands + ncbandsincluded - 1; + + arma::cx_vec coefskq, coefsk; + arma::cx_vec coefskq_c, coefsk_v; + + std::complex term_aux = 0.; + std::complex term_aux_2 = 0.; + std::complex g_s = this->g_s; // Spin degeneracy + + if (arma::norm(q) < 1E-7 && (arma::norm(G) < 1E-7 || arma::norm(G2) < 1E-7)){ + return 0.; + } + + if (this->eigveckqStack_.is_empty() && this->eigvalkqStack_.is_empty()) { + std::cout << "Bloch Hamiltonian has to be diagonalized at every k+q point before computing polarizability matrix elements. Terminating" << std::endl; + exit(0); + } + + for (int ic = nvbands; ic <= upperindexcband; ic++){ + + for (int iv = nvbands - 1; iv >= nvbands - nvbandsincluded; iv--){ + + for (uint ik = 0; ik < nk; ik++){ + + arma::rowvec k = this->kpoints_aux.row(ik); + arma::rowvec kq = k + q; + + // Using the atomic gauge + if(gauge == "atomic"){ + coefskq = system_->latticeToAtomicGauge(eigveckqStack_.slice(ik).col(iv), kq); + coefsk = system_->latticeToAtomicGauge(eigveckStack_.slice(ik).col(ic), k); + + coefskq_c = system_->latticeToAtomicGauge(eigveckqStack_.slice(ik).col(ic), kq); + coefsk_v = system_->latticeToAtomicGauge(eigveckStack_.slice(ik).col(iv), k); + } + else{ + coefskq = eigveckqStack_.slice(ik).col(iv); + coefsk = eigveckStack_.slice(ik).col(ic); + + coefskq_c = eigveckqStack_.slice(ik).col(ic); + coefsk_v = eigveckStack_.slice(ik).col(iv); + } + + std::complex IvcG_d = blochCoherenceFactor(coefsk_v, coefskq_c, kq, k, G, d); + std::complex IcvG_d = blochCoherenceFactor(coefsk, coefskq, kq, k, G, d); + + std::complex IvcG2_d = blochCoherenceFactor(coefsk_v, coefskq_c, kq, k, G2, d); + std::complex IcvG2_d = blochCoherenceFactor(coefsk, coefskq, kq, k, G2, d); + + + term_aux += IvcG_d*std::conj(IvcG2_d) / (eigvalkStack_.col(ik)(iv) - eigvalkqStack_.col(ik)(ic)); + term_aux_2 += IcvG_d*std::conj(IcvG2_d) / (eigvalkStack_.col(ik)(ic) - eigvalkqStack_.col(ik)(iv)); + } + } + } + + return g_s*(term_aux - term_aux_2)/((std::complex)nk); +} + +/** + * Method to compute the (G,G') matrix element of the static 2D dielectric matrix at the specified arbitrary momentum vector q. + * @details The purely 2D polarizability is computed + * @param G Reciprocal lattice vector G + * @param G2 Reciprocal lattice vector G2 + * @param q Momentum vector q + * @return Polarizability +*/ +std::complex ExcitonTB::compute_2D_DielectricMatrixElement(const arma::rowvec& G, const arma::rowvec& G2, const arma::rowvec& q) { + + double kroneckerdelta = arma::norm(G - G2) < 10E-7 ? 1 : 0; + + const double potential = coulomb_2D_FT(q + G)*coulomb_2D_FT(q + G2); + + std::complex epsilon = kroneckerdelta - potential*this->compute_2D_PolarizabilityMatrixElement(q,G,G2); + + return epsilon; +} + +/** + * Method to compute the (G,G') matrix element of the quasi-2D dielectric matrix at the specified arbitrary momentum vector q (divided by d). + * @details The dielectric matrix as function of (z,z') averaged over the thickness d of the material is computed + * @param G Reciprocal lattice vector G + * @param G2 Reciprocal lattice vector G2 + * @param q Momentum vector q + * @param d 2D material thickness + * @return Polarizability + */ +std::complex ExcitonTB::compute_quasi2D_DielectricMatrixElement(const arma::rowvec &G, const arma::rowvec &G2, const arma::rowvec &q, const double d) { + + double potential = std::sqrt(coulomb_2D_FT(q + G))*std::sqrt(coulomb_2D_FT(q + G2)); + + double kroneckerdelta = arma::norm(G - G2) < 10E-7 ? 1 : 0; + + std::complex epsilon = kroneckerdelta - potential*compute_quasi2D_PolarizabilityMatrixElement(q, G, G2, d); + + return epsilon; +} + +/** + * Method to compute the (G,G') static 2D polarizability in the BZ mesh. + * @details Opens 'polarizability_mesh.dat' file and writes in it the values of the polarizability at each point in the BZ mesh + * @return void +*/ +void ExcitonTB::PolarizabilityMesh() { + + auto start = high_resolution_clock::now(); + + if (this->mode == "realspace"){ + std::cout << "Numerical screening in real space not implemented. Terminating." << std::flush; + exit(0); + } + + if (this->mode == "reciprocalspace"){ + std::cout << "Computing polarizability in the BZ mesh... \n" << std::flush; + + std::ofstream polarfile; + + polarfile.open("polarizability_mesh.dat"); + + if (!polarfile.is_open()) { // check if the file was opened successfully + std::cerr << "Error opening file\n"; + std::cerr << errno << "\n"; + + exit(1); + } + + uint nq = system->nk; + uint nk_aux = this->nk_aux; + int basisdim = system->basisdim; + + arma::cx_vec Chi(nq, arma::fill::zeros); + + arma::mat reciprocalVectors = this->trunreciprocalLattice_; + + arma::rowvec g = reciprocalVectors.row(this->Gs(0)); // Sets G + arma::rowvec g2 = reciprocalVectors.row(this->Gs(1)); // Sets G' + + if (this->eigveckqStack_.is_empty() && this->eigvalkqStack_.is_empty()) { + this->eigveckqStack_ = arma::cx_cube(basisdim, basisdim, nk_aux); + this->eigvalkqStack_ = arma::mat(basisdim, nk_aux); + } + + #pragma omp parallel for + for (uint iq = 0; iq < nq; iq++){ + + vec auxEigVal(basisdim); + arma::cx_mat auxEigvec(basisdim, basisdim); + + arma::rowvec q = system->kpoints.row(iq); + + for (uint i = 0; i < nk_aux; i++) + { + arma::rowvec kq = this->kpoints_aux.row(i) + q; + system->solveBands(kq, auxEigVal, auxEigvec); + auxEigvec = fixGlobalPhase(auxEigvec); + this->eigvalkqStack_.col(i) = auxEigVal; + this->eigveckqStack_.slice(i) = auxEigvec; + }; + + Chi(iq) = this->compute_2D_PolarizabilityMatrixElement(g, g2, q); + } + + std::cout << "\n Chi computed" << std::endl; + + for (uint iq = 0; iq < nq; iq++){ + auto q = system_->kpoints.row(iq); + polarfile << q(0) << " " << q(1) << " " << q(2) << " " << real(Chi(iq)) << " " << imag(Chi(iq)) << "\n"; + } + + polarfile.close(); + } + + auto stop = high_resolution_clock::now(); + auto duration = duration_cast(stop - start); + + std::cout << "Done in " << duration.count()/1000.0 << " s." << std::endl; +} + +/** + * Method to fetch the index of a reciprocal lattice vector. + * @details returns -1 if not found. + * @return int +*/ +int ExcitonTB::fetchReciprocalLatticeVector(arma::rowvec G){ + + uint nGs = this->trunreciprocalLattice_.n_rows; + + for (uint i = 0; i < nGs; ++i){ + if (arma::norm(G - this->trunreciprocalLattice_.row(i)) < 1E-7){ + return i; + } + } + + std::cout << "Reciprocal lattice vector G = (" << G(0) << ", " << G(1) << ") not found in the reciprocal lattice." << std::endl; + + return -1; // G not found +} + +/** + * Method to compute the static 2D dielectric matrix in the BZ mesh. + * @return void +*/ +void ExcitonTB::compute_2D_DielectricMatrix(){ + + auto start = high_resolution_clock::now(); + + if (this->mode == "realspace"){ + std::cout << "Numerical screening in real space not implemented. Terminating" << std::endl; + exit(0); + } + + if (this->mode == "reciprocalspace"){ + + arma::mat ReciprocalVectors = this->trunreciprocalLattice_; + uint nGs = ReciprocalVectors.n_rows; + uint Ncells = this->ncell_; + uint odd = Ncells % 2; + uint nq = odd == 1 ? Ncells * (Ncells - odd) / 2 + (Ncells - odd) / 2 + 1 : (2 * Ncells - 1) + (Ncells - 1) * (Ncells - 2) / 2 + Ncells / 2 + 1; // Only half of the BZ + + std::cout << "\nNumber of G vectors included in the calculation of the screening: " << nGs << std::endl; + + this->setq_points_list(system->kpoints); // The set of q points where the dielectric matrix is computed coincides with the BZ mesh + uint Nqpoints = this->qpoints_list_.n_rows; + arma::mat q_points(Nqpoints, 3, arma::fill::zeros); + + uint nk_aux = this->nk_aux; + uint Nktotal = system->nk; + + q_points = this->qpoints_list_; + uint nq_count = 0; + uint basisdim = system->basisdim; + + double d = this->d; + bool is_d_finite = std::abs(d) > 1E-4; + + std::cout << "Diagonalizing H(k+q) for every point q, for every point k... " << std::flush; + + // In case the polarizability/dielectric matrix has been computed before with another routine, reshape to account for a different number of q points + if (this->eigvalkqStack_test.is_empty() || this->eigveckqStack_test.empty()) + { + this->eigvalkqStack_test = arma::cube(basisdim, nk_aux, Nqpoints, arma::fill::zeros); + + std::vector vector_aux; + vector_aux.resize(Nqpoints); + this->eigveckqStack_test = vector_aux; + + for (uint iq = 0; iq < Nqpoints; ++iq) + { + this->eigveckqStack_test[iq] = arma::cx_cube(basisdim, basisdim, nk_aux, arma::fill::zeros); + } + } + else + { + this->eigvalkqStack_test.set_size(basisdim, nk_aux, Nqpoints); + this->eigveckqStack_test.resize(Nqpoints); + + for (uint iq = 0; iq < Nqpoints; ++iq) + { + this->eigveckqStack_test[iq] = arma::cx_cube(basisdim, basisdim, nk_aux, arma::fill::zeros); + } + } + + arma::vec auxEigVal(basisdim); + arma::cx_mat auxEigvec(basisdim, basisdim); + + for (uint iq = 0; iq < Nqpoints; ++iq) + { + arma::rowvec q = q_points.row(iq); + + for (uint i = 0; i < nk_aux; i++) + { + arma::rowvec kq = this->kpoints_aux.row(i) + q; + system->solveBands(kq, auxEigVal, auxEigvec); + + auxEigvec = fixGlobalPhase(auxEigvec); + this->eigvalkqStack_test.slice(iq).col(i) = auxEigVal; + this->eigveckqStack_test[iq].slice(i) = auxEigvec; + }; + + } + + std::cout << "\nDone. \nCalculation of the dielectric matrix in the BZ mesh at... \n" << std::flush; + + arma::cx_mat auxvecsol(nGs,nGs,arma::fill::zeros); + arma::cx_mat auxvec(nGs,nGs,arma::fill::eye); + + arma::imat indecesqg(nq*nGs*(nGs+1)/2,3,arma::fill::zeros); + + if (odd == 0){ // If Ncells is even, then q points at the boundaries of the BZ with no symmetric counterpart are computed separately + int i=0; + + for (uint iq = 0; iq < Ncells; iq++){ // 1st BZ boundary + for (uint g = 0; g < nGs; g++){ + for (uint g2 = g; g2 < nGs; g2++){ + indecesqg.row(i)(0) = iq; + indecesqg.row(i)(1) = g; + indecesqg.row(i)(2) = g2; + i++; + } + } + } + + for (uint iq = 1; iq < Ncells; iq++){ // 2nd BZ boundary + for (uint g = 0; g < nGs; g++){ + for (uint g2 = g; g2 < nGs; g2++){ + indecesqg.row(i)(0) = iq*Ncells; + indecesqg.row(i)(1) = g; + indecesqg.row(i)(2) = g2; + i++; + } + } + } + + for (uint iq = 1; iq < Ncells/2; iq++){ // Centrosymmetric submesh of the whole BZ mesh + for (uint iq2 = 1; iq2 < Ncells; iq2++){ + for (uint g = 0; g < nGs; g++){ + for (uint g2 = g; g2 < nGs; g2++){ + indecesqg.row(i)(0) = iq2 + iq*Ncells; + indecesqg.row(i)(1) = g; + indecesqg.row(i)(2) = g2; + i++; + } + } + } + } + + for (uint iq = 0; iq < Ncells/2; iq++){ // Centrosymmetric submesh of the whole BZ mesh + for (uint g = 0; g < nGs; g++){ + for (uint g2 = g; g2 < nGs; g2++){ + indecesqg.row(i)(0) = 1 + iq + Ncells*Ncells/2; + indecesqg.row(i)(1) = g; + indecesqg.row(i)(2) = g2; + i++; + } + } + } + } else if (odd == 1) { // If Ncells is odd, the full BZ mesh is automatically centrosymmetric + int i=0; + + for (uint iq = 0; iq < nq; iq++){ + for (uint g = 0; g < nGs; g++){ + for (uint g2 = g; g2 < nGs; g2++){ + indecesqg.row(i)(0) = iq; + indecesqg.row(i)(1) = g; + indecesqg.row(i)(2) = g2; + i++; + } + } + } + } + + if (odd == 0){ + uint iq_test = 0; + arma::rowvec q_test = q_points.row(iq_test); + + for (uint ik = 0; ik < (2 * Ncells - 1); ik++) + { + uint iq = indecesqg.row(ik*nGs*(nGs+1)/2)(0); + arma::rowvec q = q_points.row(iq); + + this->eigvalkqStack_ = this->eigvalkqStack_test.slice(iq); + this->eigveckqStack_ = this->eigveckqStack_test[iq]; + + #pragma omp parallel for + for (uint ig = 0; ig < nGs * (nGs + 1) / 2; ig++) + { + uint g = indecesqg.row(ig)(1); + uint g2 = indecesqg.row(ig)(2); + + arma::rowvec G = ReciprocalVectors.row(g); + arma::rowvec G2 = ReciprocalVectors.row(g2); + + std::complex Chi = 0.0; + + if (is_d_finite) { + Chi = compute_quasi2D_PolarizabilityMatrixElement(q, G, G2, d); + } + else { + Chi = compute_2D_PolarizabilityMatrixElement(q, G, G2); + } + + double potentialg = std::sqrt(coulomb_2D_FT(q + G)) * std::sqrt(coulomb_2D_FT(q + G2)); + double potentialg2 = potentialg; + + this->Chimatrix_.slice(iq).row(g)(g2) = Chi; + this->Chimatrix_.slice(iq).row(g2)(g) = std::conj(Chi); + + double kroneckerdelta = g == g2 ? 1 : 0; + + this->epsilonmatrix_.slice(iq).row(g)(g2) = kroneckerdelta - potentialg * Chi; + this->epsilonmatrix_.slice(iq).row(g2)(g) = kroneckerdelta - potentialg2 * std::conj(Chi); + } + nq_count++; + } + + uint iq_i = (2 * Ncells - 1); + uint ik_f = (Ncells - 1)*(Ncells - 2)/2 + Ncells/2; + + for (uint ik = 0; ik < ik_f; ik++) + { + uint iq = indecesqg.row(iq_i*nGs*(nGs + 1)/2 + ik*nGs*(nGs + 1)/2)(0); // indecesqg.row(i_aux)(0); + arma::rowvec q = q_points.row(iq); + + this->eigvalkqStack_ = this->eigvalkqStack_test.slice(iq); + this->eigveckqStack_ = this->eigveckqStack_test[iq]; + + uint negativeqindex = -1; + + for (uint i = 0; i < Nqpoints; ++i) + { + if (arma::norm(q + q_points.row(i)) < 1E-7) + { + negativeqindex = i; + break; + } + } + + #pragma omp parallel for + for (uint ig = 0; ig < nGs * (nGs + 1) / 2; ig++) + { + //uint iq = ik; //indecesqg.row(i_aux)(0); + uint g = indecesqg.row(ig)(1); + uint g2 = indecesqg.row(ig)(2); + + arma::rowvec G = ReciprocalVectors.row(g); + arma::rowvec G2 = ReciprocalVectors.row(g2); + + uint negativeG = fetchReciprocalLatticeVector(-G); + uint negativeG2 = fetchReciprocalLatticeVector(-G2); + + std::complex Chi = 0.0; + + if (is_d_finite) { + Chi = compute_quasi2D_PolarizabilityMatrixElement(q, G, G2, d); + } + else { + Chi = compute_2D_PolarizabilityMatrixElement(q, G, G2); + } + + this->Chimatrix_.slice(iq).row(g)(g2) = Chi; + this->Chimatrix_.slice(iq).row(g2)(g) = std::conj(Chi); + + this->Chimatrix_.slice(negativeqindex).row(negativeG2)(negativeG) = Chi; + this->Chimatrix_.slice(negativeqindex).row(negativeG)(negativeG2) = std::conj(Chi); + + double potentialg = std::sqrt(coulomb_2D_FT(q + G)) * std::sqrt(coulomb_2D_FT(q + G2)); + double potentialg2 = potentialg; + + double potentialnegativeG = std::sqrt(coulomb_2D_FT(system->kpoints.row(negativeqindex) - G)) * std::sqrt(coulomb_2D_FT(system->kpoints.row(negativeqindex) - G2)); + double potentialnegativeG2 = potentialnegativeG; + double kroneckerdelta = g == g2 ? 1 : 0; + + this->epsilonmatrix_.slice(iq).row(g)(g2) = kroneckerdelta - potentialg * this->Chimatrix_.slice(iq).row(g)(g2); + this->epsilonmatrix_.slice(iq).row(g2)(g) = kroneckerdelta - potentialg2 * std::conj(Chi); + + this->epsilonmatrix_.slice(negativeqindex).row(negativeG2)(negativeG) = kroneckerdelta - potentialnegativeG2 * Chi; + this->epsilonmatrix_.slice(negativeqindex).row(negativeG)(negativeG2) = kroneckerdelta - potentialnegativeG * std::conj(Chi); + } + + int nq_count_aux = nq_count + 1; + double percentage_aux = 2*(double)nq_count_aux/nq*100.0; + double percentage = 2*(double)nq_count/nq*100.0; + + if (((int) percentage_aux != (int) percentage) && ((int) percentage) % 5 == 0) { + std::cout << (int) percentage << "%" << std::endl; + } + nq_count++; + } + } + + if (odd == 1){ + + for (uint ik = 0; ik < nq; ik++) + { + uint iq = indecesqg.row(ik*nGs*(nGs + 1)/2)(0); + arma::rowvec q = q_points.row(iq); + + this->eigvalkqStack_ = this->eigvalkqStack_test.slice(iq); + this->eigveckqStack_ = this->eigveckqStack_test[iq]; + + #pragma omp parallel for + for (uint ig = 0; ig < nGs * (nGs + 1) / 2; ig++) + { + uint g = indecesqg.row(ig)(1); + uint g2 = indecesqg.row(ig)(2); + + arma::rowvec G = ReciprocalVectors.row(g); + arma::rowvec G2 = ReciprocalVectors.row(g2); + arma::rowvec q = q_points.row(iq); + + uint negativeG = fetchReciprocalLatticeVector(-G); + uint negativeG2 = fetchReciprocalLatticeVector(-G2); + + this->eigvalkqStack_ = this->eigvalkqStack_test.slice(iq); + this->eigveckqStack_ = this->eigveckqStack_test[iq]; + + std::complex Chi = 0.0; + + if (is_d_finite) { + Chi = compute_quasi2D_PolarizabilityMatrixElement(q, G, G2, d); + } + else { + Chi = compute_2D_PolarizabilityMatrixElement(q, G, G2); + } + + this->Chimatrix_.slice(iq).row(g)(g2) = Chi; + this->Chimatrix_.slice(iq).row(g2)(g) = std::conj(Chi); + + this->Chimatrix_.slice(Nktotal - iq - 1).row(negativeG2)(negativeG) = Chi; + this->Chimatrix_.slice(Nktotal - iq - 1).row(negativeG)(negativeG2) = std::conj(Chi); + + double potentialg = std::sqrt(coulomb_2D_FT(q + G)) * std::sqrt(coulomb_2D_FT(q + G2)); + double potentialg2 = potentialg; + + double potentialnegativeG = std::sqrt(coulomb_2D_FT(q_points.row(Nktotal - iq - 1)-G)) * std::sqrt(coulomb_2D_FT(q_points.row(Nktotal - iq - 1)-G2)); + double potentialnegativeG2 = potentialnegativeG; + + double kroneckerdelta = g == g2 ? 1 : 0; + + this->epsilonmatrix_.slice(iq).row(g)(g2) = kroneckerdelta - potentialg * Chi; + this->epsilonmatrix_.slice(iq).row(g2)(g) = kroneckerdelta - potentialg2 * std::conj(Chi); + + this->epsilonmatrix_.slice(Nktotal - iq - 1).row(negativeG2)(negativeG) = kroneckerdelta - potentialnegativeG2 * Chi; + this->epsilonmatrix_.slice(Nktotal - iq - 1).row(negativeG)(negativeG2) = kroneckerdelta - potentialnegativeG * std::conj(Chi); + } + + int nq_count_aux = nq_count + 1; + double percentage_aux = 2*(double)nq_count_aux/nq*100.0; + double percentage = 2*(double)nq_count/nq*100.0; + + if (((int) percentage_aux != (int) percentage) && ((int) percentage) % 5 == 0) { + std::cout << (int) percentage << "%" << std::endl; + } + nq_count++; + } + } + } + + + auto stop_dielectric_matrix_mesh = high_resolution_clock::now(); + auto duration_dielectric_matrix_mesh = duration_cast(stop_dielectric_matrix_mesh - start); + + std::cout << ") Done. \nCalculation of dielectric matrix completed in " << duration_dielectric_matrix_mesh.count()/1000.0 << " s." << std::endl << std::flush; +} + +/** + * Method to augment the static 2D dielectric matrix in the BZ mesh. + * @return void +*/ +void ExcitonTB::augment_2D_DielectricMatrix(double Gcutoff){ + + auto start = high_resolution_clock::now(); + + if (this->mode == "realspace"){ + std::cout << "Numerical screening in real space not available. Terminating" << std::endl; + exit(0); + } + + if (this->mode == "reciprocalspace"){ + + uint Ncells = this->ncell_; + uint odd = Ncells % 2; + uint nq = odd == 1 ? Ncells * (Ncells - odd) / 2 + (Ncells - odd) / 2 + 1 : (2 * Ncells - 1) + (Ncells - 1) * (Ncells - 2) / 2 + Ncells / 2 + 1; // Only half of the BZ + + std::cout << "Number of G vectors included in the calculation: " << nGs << std::endl; + printReciprocalLattice(); + + this->setq_points_list(system->kpoints); // The set of q points where the dielectric matrix is computed coincides with the BZ mesh + uint Nqpoints = this->qpoints_list_.n_rows; + arma::mat q_points(Nqpoints, 3, arma::fill::zeros); + + uint nk_aux = this->nk_aux; + uint Nktotal = system->nk; + + q_points = this->qpoints_list_; + + uint basisdim = system->basisdim; + + double d = this->d_; + bool is_d_finite = std::abs(d) > 1E-4; + + if (this->Invepsilonmatrix_.is_empty()) + { + std::cout << "No inverse dielectric matrix exists. One must be provided before augmenting it. Terminating." << std::endl; + exit(0); + } + + uint nq_points = this->Invepsilonmatrix_.n_slices; + + if (nq_points != Nqpoints) + { + std::cout << "The number of q points in the provided inverse dielectric matrix does not match the number of q points in the BZ mesh. Terminating." << std::endl; + exit(0); + } + + arma::cx_cube Invepsilonmatrix_provided = this->Invepsilonmatrix_; + + if (this->epsilonmatrix_.is_empty()) + { + this->epsilonmatrix_ = arma::cx_cube(Invepsilonmatrix_provided.n_rows, Invepsilonmatrix_provided.n_cols, Invepsilonmatrix_provided.n_slices, arma::fill::zeros); + } + else + { + if (this->epsilonmatrix_.n_rows != Invepsilonmatrix_provided.n_rows || this->epsilonmatrix_.n_cols != Invepsilonmatrix_provided.n_cols || this->epsilonmatrix_.n_slices != Invepsilonmatrix_provided.n_slices) + { + this->epsilonmatrix_.reshape(Invepsilonmatrix_provided.n_rows, Invepsilonmatrix_provided.n_cols, Invepsilonmatrix_provided.n_slices); + } + } + + std::cout << "Inverting the provided inverse dielectric matrix... " << std::flush; + for (uint iq = 0; iq < Nqpoints; iq++) // inverts the inverse dielectric matrix to obtain the direct dielectric matrix + { + this->epsilonmatrix_.slice(iq) = arma::inv(Invepsilonmatrix_provided.slice(iq)); + } + std::cout << "Done." << std::endl; + + arma::cx_cube dielectricmatrix_provided = this->epsilonmatrix_; + + uint nGs_existing = this->Invepsilonmatrix_.slice(0).n_rows; + + setGcutoff(Gcutoff); + + arma::mat ReciprocalVectors = this->trunreciprocalLattice_; + uint nGs_new = ReciprocalVectors.n_rows; + + if (nGs_existing >= nGs_new) + { + std::cout << "The cutoff of the augmented dielectric matrix has to be higher than the existing one. Terminating." << std::endl; + exit(0); + } + + this->Chimatrix_.reshape(nGs_new, nGs_new, Nqpoints); + this->epsilonmatrix_.reshape(nGs_new, nGs_new, Nqpoints); + this->Invepsilonmatrix_.reshape(nGs_new, nGs_new, Nqpoints); + + for (uint iq = 0; iq < Nqpoints; iq++) + { + this->epsilonmatrix_.slice(iq).submat(arma::span(0, nGs_existing - 1), arma::span(0, nGs_existing - 1)) = dielectricmatrix_provided.slice(iq); + } + arma::cx_mat auxvecsol(nGs_new,nGs_new,arma::fill::zeros); + arma::cx_mat auxvec(nGs_new,nGs_new,arma::fill::eye); + uint nGs_new_combinations = nGs_existing*(nGs_new-nGs_existing) + (nGs_new-nGs_existing)*(nGs_new-nGs_existing+1)/2; + arma::imat indecesqg(nq*nGs_new_combinations,3,arma::fill::zeros); + + std::cout << "Number of extra GG' combinations to compute: " << nGs_new_combinations << std::endl; + std::cout << "Diagonalizing H(k+q) for every point q, for every point k... " << std::flush; + + if (this->eigvalkqStack_test.is_empty() || this->eigveckqStack_test.empty()) + { + this->eigvalkqStack_test = arma::cube(basisdim, nk_aux, Nqpoints, arma::fill::zeros); + + std::vector vector_aux; + vector_aux.resize(Nqpoints); + this->eigveckqStack_test = vector_aux; + + for (uint iq = 0; iq < Nqpoints; ++iq) + { + this->eigveckqStack_test[iq] = arma::cx_cube(basisdim, basisdim, nk_aux, arma::fill::zeros); + } + } + else + { + this->eigvalkqStack_test.set_size(basisdim, nk_aux, Nqpoints); + this->eigveckqStack_test.resize(Nqpoints); + + for (uint iq = 0; iq < Nqpoints; ++iq) + { + this->eigveckqStack_test[iq] = arma::cx_cube(basisdim, basisdim, nk_aux, arma::fill::zeros); + } + } + + arma::vec auxEigVal(basisdim); + arma::cx_mat auxEigvec(basisdim, basisdim); + + std::cout << "q point " << std::flush; + + for (uint iq = 0; iq < Nqpoints; ++iq) + { + arma::rowvec q = q_points.row(iq); + + for (uint i = 0; i < nk_aux; i++) + { + arma::rowvec kq = this->kpoints_aux.row(i) + q; + system->solveBands(kq, auxEigVal, auxEigvec); + + auxEigvec = fixGlobalPhase(auxEigvec); + this->eigvalkqStack_test.slice(iq).col(i) = auxEigVal; + this->eigveckqStack_test[iq].slice(i) = auxEigvec; + } + + std::cout << iq + 1 << ", " << std::flush; + if ((iq + 1) % 150 == 0) { + std::cout << std::endl; + } + } + + std::cout << "\nDone. \nComputing the remaining dielectric function matrix elements in the BZ mesh... \n" << std::flush; + + if (odd == 0){ // If Ncells is even, then q points at the boundaries of the BZ with no symmetric counterpart are computed seperately + int i=0; + + for (uint iq = 0; iq < Ncells; iq++){ // 1st BZ boundary, right block the dielectric matrix + for (uint g = nGs_existing; g < nGs_new; g++){ + for (uint g2 = 0; g2 <= g; g2++){ + indecesqg.row(i)(0) = iq; + indecesqg.row(i)(1) = g; + indecesqg.row(i)(2) = g2; + i++; + } + } + } + + for (uint iq = 1; iq < Ncells; iq++){ // 2nd BZ boundary, right block the dielectric matrix + for (uint g = nGs_existing; g < nGs_new; g++){ + for (uint g2 = 0; g2 <= g; g2++){ + indecesqg.row(i)(0) = iq*Ncells; + indecesqg.row(i)(1) = g; + indecesqg.row(i)(2) = g2; + i++; + } + } + } + + for (uint iq = 1; iq < Ncells/2; iq++){ // Centro-symmetric submesh of the full BZ mesh, right block the dielectric matrix + for (uint iq2 = 1; iq2 < Ncells; iq2++){ + for (uint g = nGs_existing; g < nGs_new; g++){ + for (uint g2 = 0; g2 <= g; g2++){ + indecesqg.row(i)(0) = iq2 + iq*Ncells; + indecesqg.row(i)(1) = g; + indecesqg.row(i)(2) = g2; + i++; + } + } + } + } + + for (uint iq = 0; iq < Ncells/2; iq++){ // Centro-symmetric submesh of the full BZ mesh, right block of the dielectric matrix + for (uint g = nGs_existing; g < nGs_new; g++){ + for (uint g2 = 0; g2 <= g; g2++){ + indecesqg.row(i)(0) = 1 + iq + Ncells*Ncells/2; + indecesqg.row(i)(1) = g; + indecesqg.row(i)(2) = g2; + i++; + } + } + } + + } else if (odd == 1) { // If Ncells is odd, the full BZ mesh is automatically center-symmetric + int i=0; + + for (uint iq = 0; iq < nq; iq++){ + for (uint g = nGs_existing; g < nGs_new; g++){ + for (uint g2 = 0; g2 <= g; g2++){ + indecesqg.row(i)(0) = iq; + indecesqg.row(i)(1) = g; + indecesqg.row(i)(2) = g2; + i++; + } + } + } + } + + if (odd == 0){ + + uint iq_test = 0; + arma::rowvec q_test = q_points.row(iq_test); + + for (uint ik = 0; ik < (2 * Ncells - 1); ik++) + { + uint iq = indecesqg.row(ik*nGs_new_combinations)(0); + arma::rowvec q = q_points.row(iq); + + this->eigvalkqStack_ = this->eigvalkqStack_test.slice(iq); + this->eigveckqStack_ = this->eigveckqStack_test[iq]; + + #pragma omp parallel for + for (uint ig = 0; ig < nGs_new_combinations; ig++) + { + uint g = indecesqg.row(ig)(1); + uint g2 = indecesqg.row(ig)(2); + + arma::rowvec G = ReciprocalVectors.row(g); + arma::rowvec G2 = ReciprocalVectors.row(g2); + + std::complex Chi = 0.0; + + if (is_d_finite) { + Chi = compute_quasi2D_PolarizabilityMatrixElement(q, G, G2, d); + } + else { + Chi = compute_2D_PolarizabilityMatrixElement(q, G, G2); + } + double potentialg = std::sqrt(coulomb_2D_FT(q + G)) * std::sqrt(coulomb_2D_FT(q + G2)); + + double kroneckerdelta = g == g2 ? 1 : 0; + + std::complex epsilon_gg2_element = kroneckerdelta - potentialg * Chi; + + this->epsilonmatrix_.slice(iq).row(g)(g2) = epsilon_gg2_element; + this->epsilonmatrix_.slice(iq).row(g2)(g) = std::conj(epsilon_gg2_element); + } + } + + // Computes the dielectric matrix at the centrosymmetric submesh of the BZ + + uint iq_i = (2 * Ncells - 1); + uint ik_f = (Ncells - 1)*(Ncells - 2)/2 + Ncells/2; + for (uint ik = 0; ik < ik_f; ik++) + { + uint iq = indecesqg.row(iq_i*nGs_new_combinations + ik*nGs_new_combinations)(0); + arma::rowvec q = q_points.row(iq); + + this->eigvalkqStack_ = this->eigvalkqStack_test.slice(iq); + this->eigveckqStack_ = this->eigveckqStack_test[iq]; + + uint negativeqindex = -1; + + for (uint i = 0; i < Nqpoints; ++i) + { + if (arma::norm(q + q_points.row(i)) < 1E-7) + { + negativeqindex = i; + break; + } + } + + #pragma omp parallel for + for (uint ig = 0; ig < nGs_new_combinations; ig++) + { + uint g = indecesqg.row(ig)(1); + uint g2 = indecesqg.row(ig)(2); + + arma::rowvec G = ReciprocalVectors.row(g); + arma::rowvec G2 = ReciprocalVectors.row(g2); + + uint negativeG = fetchReciprocalLatticeVector(-G); + uint negativeG2 = fetchReciprocalLatticeVector(-G2); + + std::complex Chi = 0.0; + if (is_d_finite) { + Chi = compute_quasi2D_PolarizabilityMatrixElement(q, G, G2, d); + } + else { + Chi = compute_2D_PolarizabilityMatrixElement(q, G, G2); + } + + double potentialg = std::sqrt(coulomb_2D_FT(q + G)) * std::sqrt(coulomb_2D_FT(q + G2)); + double potentialg2 = potentialg; + + double potentialnegativeG = std::sqrt(coulomb_2D_FT(system->kpoints.row(negativeqindex) - G)) * std::sqrt(coulomb_2D_FT(system->kpoints.row(negativeqindex) - G2)); + double potentialnegativeG2 = potentialnegativeG; + + double kroneckerdelta = g == g2 ? 1 : 0; + + this->epsilonmatrix_.slice(iq).row(g)(g2) = kroneckerdelta - potentialg * Chi; + this->epsilonmatrix_.slice(iq).row(g2)(g) = kroneckerdelta - potentialg2 * std::conj(Chi); + + this->epsilonmatrix_.slice(negativeqindex).row(negativeG2)(negativeG) = kroneckerdelta - potentialnegativeG2 * Chi; + this->epsilonmatrix_.slice(negativeqindex).row(negativeG)(negativeG2) = kroneckerdelta - potentialnegativeG * std::conj(Chi); + } + } + } + + if (odd == 1){ + + for (uint ik = 0; ik < nq; ik++) + { + uint iq = indecesqg.row(ik*nGs_new_combinations)(0); + arma::rowvec q = q_points.row(iq); + + this->eigvalkqStack_ = this->eigvalkqStack_test.slice(iq); + this->eigveckqStack_ = this->eigveckqStack_test[iq]; + + #pragma omp parallel for + for (uint ig = 0; ig < nGs_new_combinations; ig++) + { + uint g = indecesqg.row(ig)(1); + uint g2 = indecesqg.row(ig)(2); + + arma::rowvec G = ReciprocalVectors.row(g); + arma::rowvec G2 = ReciprocalVectors.row(g2); + arma::rowvec q = q_points.row(iq); + + uint negativeG = fetchReciprocalLatticeVector(-G); + uint negativeG2 = fetchReciprocalLatticeVector(-G2); + + this->eigvalkqStack_ = this->eigvalkqStack_test.slice(iq); + this->eigveckqStack_ = this->eigveckqStack_test[iq]; + + std::complex Chi = 0.0; + if (is_d_finite) { + Chi = compute_quasi2D_PolarizabilityMatrixElement(q, G, G2, d); + } + else { + Chi = compute_2D_PolarizabilityMatrixElement(q, G, G2); + } + + this->Chimatrix_.slice(iq).row(g)(g2) = Chi; + this->Chimatrix_.slice(iq).row(g2)(g) = std::conj(Chi); + + this->Chimatrix_.slice(Nktotal - iq - 1).row(negativeG2)(negativeG) = Chi; + this->Chimatrix_.slice(Nktotal - iq - 1).row(negativeG)(negativeG2) = std::conj(Chi); + + double potentialg = std::sqrt(coulomb_2D_FT(q + G)) * std::sqrt(coulomb_2D_FT(q + G2)); + double potentialg2 = potentialg; + + double potentialnegativeG = std::sqrt(coulomb_2D_FT(q_points.row(Nktotal - iq - 1) - G)) * std::sqrt(coulomb_2D_FT(q_points.row(Nktotal - iq - 1) - G2)); + double potentialnegativeG2 = potentialnegativeG; + + double kroneckerdelta = g == g2 ? 1 : 0; + + this->epsilonmatrix_.slice(iq).row(g)(g2) = kroneckerdelta - potentialg * Chi; + this->epsilonmatrix_.slice(iq).row(g2)(g) = kroneckerdelta - potentialg2 * std::conj(Chi); + + this->epsilonmatrix_.slice(Nktotal - iq - 1).row(negativeG2)(negativeG) = kroneckerdelta - potentialnegativeG2 * Chi; + this->epsilonmatrix_.slice(Nktotal - iq - 1).row(negativeG)(negativeG2) = kroneckerdelta - potentialnegativeG * std::conj(Chi); + } + } + } + } + + auto stop_dielectric_matrix_mesh = high_resolution_clock::now(); + auto duration_dielectric_matrix_mesh = duration_cast(stop_dielectric_matrix_mesh - start); + + std::cout << "Done. \nCalculation of dielectric matrix completed in " << duration_dielectric_matrix_mesh.count()/1000.0 << " s." << std::endl << std::flush; +} + +/** + * Method to compute the strictly 2D static polarizability matrix and dielectric matrix in a set of user specified q points. More useful for isotropic systems. + * @return void +*/ +void ExcitonTB::compute_2D_DielectricMatrix(std::string kpointsfile){ + + auto start = high_resolution_clock::now(); + + if (this->mode == "realspace"){ + + std::cout << "Numerical screening in real space not implemented. Terminating." << std::endl; + + std::exit(0); + } + + if (this->mode == "reciprocalspace"){ + + // Reads q points from file + std::ifstream inputfile(kpointsfile); + if (!inputfile) { + std::cout << "File for k points failed to open or does not exist. Exiting" << std::endl; + exit(1); + } + + std::string line; + double qx, qy, qz; + arma::mat q_points; + + double d = this->d; + bool is_d_finite = std::abs(d) > 1E-4; + + try{ + while(std::getline(inputfile, line)){ + std::istringstream iss(line); + iss >> qx >> qy >> qz; + arma::rowvec qpoint{qx, qy, qz}; + q_points.insert_rows(q_points.n_rows,qpoint); + } + inputfile.close(); + } + catch(const std::exception& e){ + std::cerr << e.what() << std::endl; + } + + setq_points_list(q_points); + + uint Nqpoints = q_points.n_rows; + + std::cout << "Computing 2D dielectric matrix in the specified q points... \n" << std::flush; + + uint nk = this->nk_aux; + uint basisdim = system->basisdim; + + arma::mat ReciprocalVectors = this->trunreciprocalLattice_; + uint nGs = ReciprocalVectors.n_rows; + + // In case the polarizability/dielectric matrix have been computed before with another routine, reshape to account for a different number of k points + if (this->Chimatrix_.is_empty()) { + this->Chimatrix_ = arma::cx_cube(nGs,nGs,Nqpoints,arma::fill::zeros); + } else { + this->Chimatrix_.reshape(nGs,nGs,Nqpoints); + } + + if (this->epsilonmatrix_.is_empty()) { + this->epsilonmatrix_ = arma::cx_cube(nGs,nGs,Nqpoints,arma::fill::zeros); + } else { + this->epsilonmatrix_.reshape(nGs,nGs,Nqpoints); + } + + arma::cx_cube epsilonmatrix(Nqpoints,nGs,nGs,arma::fill::zeros); + arma::cx_mat auxvec(nGs,nGs,arma::fill::eye); + + arma::imat indecesqg(Nqpoints*nGs*(nGs+1)/2,3,arma::fill::zeros); + + arma::imat indecesg(nGs*(nGs+1)/2,2,arma::fill::zeros); + + // Generates all the combinations of (G,G') indices + uint i = 0; + for (uint g = 0; g < nGs; g++){ + for (uint g2 = g; g2 < nGs; g2++){ + indecesqg.row(i)(0) = g; + indecesqg.row(i)(1) = g2; + i++; + } + } + + this->eigveckqStack_ = arma::cx_cube(basisdim, basisdim, nk); + this->eigvalkqStack_ = arma::mat(basisdim, nk); + vec auxEigVal(basisdim); + arma::cx_mat auxEigvec(basisdim, basisdim); + + for (uint iq = 0; iq < Nqpoints; iq++){ + + arma::rowvec q = q_points.row(iq); + + for (uint ik = 0; ik < nk; ik++){ + arma::rowvec kq = this->kpoints_aux.row(ik) + q; + system->solveBands(kq, auxEigVal, auxEigvec); + + auxEigvec = fixGlobalPhase(auxEigvec); + this->eigvalkqStack_.col(ik) = auxEigVal; + this->eigveckqStack_.slice(ik) = auxEigvec; + }; + + #pragma omp parallel for + for (uint ig = 0; ig < nGs*(nGs+1)/2; ig++){ + uint g = indecesqg.row(ig)(0); + uint g2 = indecesqg.row(ig)(1); + + arma::rowvec G = ReciprocalVectors.row(g); + arma::rowvec G2 = ReciprocalVectors.row(g2); + + std::complex Chi = 0.0; + + if (is_d_finite) { + Chi = compute_quasi2D_PolarizabilityMatrixElement(q, G, G2, d); + } + else { + Chi = compute_2D_PolarizabilityMatrixElement(q, G, G2); + } + + this->Chimatrix_.slice(iq).row(g)(g2) = Chi; + this->Chimatrix_.slice(iq).row(g2)(g) = std::conj(Chi); + + double potentialg = std::sqrt(coulomb_2D_FT(q + G)) * std::sqrt(coulomb_2D_FT(q + G2)); // double potentialg = coulomb_2D_FT(q + G); + double kroneckerdelta = g == g2? 1 : 0; + + this->epsilonmatrix_.slice(iq).row(g)(g2) = kroneckerdelta - potentialg*Chi; + this->epsilonmatrix_.slice(iq).row(g2)(g) = kroneckerdelta - potentialg*std::conj(Chi); + } + + } + + std::cout << "Done.\n" << std::endl; + } + + auto stop_dielectric_matrix_mesh = high_resolution_clock::now(); + auto duration_dielectric_matrix_mesh = duration_cast(stop_dielectric_matrix_mesh - start); + + std::cout << "Done in " << duration_dielectric_matrix_mesh.count()/1000.0 << " s." << std::endl << std::flush; +} + + +/** + * Method to compute the strictly 2D static polarizability matrix in a set of user specified q points. More useful for isotropic systems. + * @return void + */ +void ExcitonTB::compute_2D_PolarizabilityMatrix(std::string kpointsfile) +{ + auto start = high_resolution_clock::now(); + + if (this->mode == "realspace") + { + std::cout << "Screening in real space not implemented. Terminating." << std::endl; + + std::exit(0); + } + + if (this->mode == "reciprocalspace") + { + + // Reads q points from file + std::ifstream inputfile(kpointsfile); + if (!inputfile) + { + std::cout << "File for k points failed to open or does not exist. Exiting" << std::endl; + exit(1); + } + + std::string line; + double qx, qy, qz; + arma::mat q_points; + + try + { + while (std::getline(inputfile, line)) + { + std::istringstream iss(line); + iss >> qx >> qy >> qz; + arma::rowvec qpoint{qx, qy, qz}; + q_points.insert_rows(q_points.n_rows, qpoint); + } + inputfile.close(); + } + catch (const std::exception &e) + { + std::cerr << e.what() << std::endl; + } + + uint Nqpoints = q_points.n_rows; + + std::cout << "Computing polarizability matrix in the specified q points... \n" << std::flush; + + uint nk = this->nk_aux; + uint basisdim = system->basisdim; + + arma::mat ReciprocalVectors = this->trunreciprocalLattice_; + uint nGs = ReciprocalVectors.n_rows; + + this->eigveckqStack_ = arma::cx_cube(basisdim, basisdim, nk); + this->eigvalkqStack_ = arma::mat(basisdim, nk); + vec auxEigVal(basisdim); + arma::cx_mat auxEigvec(basisdim, basisdim); + + // In case the polarizability/dielectric matrix have been computed before with another routine, reshape to account for a different number of k points + if (this->Chimatrix_.is_empty()) + { + this->Chimatrix_ = arma::cx_cube(nGs, nGs, Nqpoints, arma::fill::zeros); + } + else + { + this->Chimatrix_.reshape(nGs, nGs, Nqpoints); + } + + arma::imat indecesg(nGs*(nGs + 1)/2, 2, arma::fill::zeros); + + // Generates all the combinations of (G,G') indices + uint i = 0; + for (uint g = 0; g < nGs; g++) + { + for (uint g2 = g; g2 < nGs; g2++) + { + indecesg.row(i)(0) = g; + indecesg.row(i)(1) = g2; + i++; + } + } + + for (uint iq = 0; iq < Nqpoints; iq++) + { + arma::rowvec q = q_points.row(iq); + + for (uint i = 0; i < nk; i++) + { + arma::rowvec kq = this->kpoints_aux.row(i) + q; + system->solveBands(kq, auxEigVal, auxEigvec); + + auxEigvec = fixGlobalPhase(auxEigvec); + eigvalkqStack_.col(i) = auxEigVal; + eigveckqStack_.slice(i) = auxEigvec; + }; + + #pragma omp parallel for + for (uint i = 0; i < nGs * (nGs + 1) / 2; i++) + { + int g = indecesg.row(i)(0); + int g2 = indecesg.row(i)(1); + + arma::rowvec G = ReciprocalVectors.row(g); + arma::rowvec G2 = ReciprocalVectors.row(g2); + + std::complex Chi = compute_2D_PolarizabilityMatrixElement(q, G, G2); + + this->Chimatrix_.slice(iq).row(g)(g2) = Chi; + this->Chimatrix_.slice(iq).row(g2)(g) = Chi; + } + } + + std::cout << "\n"; + } + + auto stop_dielectric_matrix_mesh = high_resolution_clock::now(); + auto duration_dielectric_matrix_mesh = duration_cast(stop_dielectric_matrix_mesh - start); + + std::cout << "Done in " << duration_dielectric_matrix_mesh.count() / 1000.0 << " s." << std::endl; +} + +/** + * Method to invert the static dielectric matrix in the list of q points. + * @return void +*/ +void ExcitonTB::invertDielectricMatrix(){ + + auto start = high_resolution_clock::now(); + + if (this->mode_ == "realspace"){ + std::cout << "Numerical screening in real space not available yet. Terminating." << std::endl; + std::exit(0); + } + + if (this->mode_ == "reciprocalspace"){ + + uint nGs = this->trunreciprocalLattice_.n_rows; + uint Nqtotal = this->epsilonmatrix_.n_slices; // The number of q points can be different from the BZ mesh size + + if (Nqtotal < 1) { + std::cout << "Dielectric matrix must have been computed at least at one point." << std::endl; + exit(0); + } + + arma::cx_mat auxvec(nGs,nGs,arma::fill::eye); + + std::cout << "\nInverting the dielectric matrix... " << std::flush; + + if (this->Invepsilonmatrix_.is_empty()) { + this->Invepsilonmatrix_ = arma::cx_cube(nGs,nGs,Nqtotal,arma::fill::zeros); + } else { + this->Invepsilonmatrix_.reshape(nGs,nGs,Nqtotal); + } + + #pragma omp parallel for + for (uint iq = 0; iq < Nqtotal; iq++){ + this->Invepsilonmatrix_.slice(iq) = arma::solve(this->epsilonmatrix_.slice(iq),auxvec); + } + } + + auto stop = high_resolution_clock::now(); + auto duration_inversion = duration_cast(stop - start); + + std::cout << "Done in " << duration_inversion.count()/1000.0 << " s." << std::endl; +} + +/** + * Method to compute the (G,G') matrix element of the static dielectric function at the specified momentum vector q. + * @details Computes the 2D version. + * @return void +*/ +std::complex ExcitonTB::computesingleDielectricFunctionMatrixElement() { + + if(mode == "realspace"){ + std::cout << "Numerical screening in real space not implemented. Terminating." << std::endl; + std::exit(0); + } + + if(mode == "reciprocalspace"){ + + std::complex Chi; + + arma::rowvec q = this->q_; + + arma::rowvec g = this->trunreciprocalLattice_.row(this->Gs_(0)); // Sets G + arma::rowvec g2 = this->trunreciprocalLattice_.row(this->Gs_(1)); // Sets G' + + uint nk = this->nk_aux; + uint nk_aux = this->nk_aux; + int basisdim = system->basisdim; + + if (this->kpoints_aux.is_empty()) { + std::cout << "Creating the coarser BZ mesh... " << std::flush; + + uint ndim = 2; + arma::mat kpoints(pow(ncell_aux, ndim), 3); + arma::mat combinations = system->generateCombinations(ncell_aux, ndim); + if (ncell_aux % 2 == 1) + { + combinations += 1. / 2; + } + + for (uint i = 0; i < nk_aux; i++) + { + arma::rowvec kpoint = arma::zeros(3); + for (uint j = 0; j < ndim; j++) + { + kpoint += (2 * combinations.row(i)(j) - ncell_aux) / (2 * ncell_aux) * system->reciprocalLattice_.row(j); + } + kpoints.row(i) = kpoint; + } + this->kpoints_aux_ = kpoints; + } + arma::mat k_points = this->kpoints_aux_; + + this->eigveckqStack_ = arma::cx_cube(basisdim, basisdim, nk); + this->eigvalkqStack_ = arma::mat(basisdim, nk); + + vec auxEigVal(basisdim); + arma::cx_mat auxEigvec(basisdim, basisdim); + + std::cout << "Diagonalizing H0 for all k+q points ... " << std::flush; + + for (uint i = 0; i < nk; i++){ + arma::rowvec kq = k_points.row(i) + q; + system->solveBands(kq, auxEigVal, auxEigvec); + + auxEigvec = fixGlobalPhase(auxEigvec); + this->eigvalkqStack_.col(i) = auxEigVal; + this->eigveckqStack_.slice(i) = auxEigvec; + }; + + Chi = computesinglePolarizabilityMatrixElement(q, g, g2); + + double potential = std::sqrt(coulomb_2D_FT(q + g))*std::sqrt(coulomb_2D_FT(q + g2)); + + std::complex kroneckerdelta = this->Gs_(0) == this->Gs_(1) ? 1. : 0.; + + std::complex epsilon = kroneckerdelta - potential*Chi; + + double d = this->d; + + std::complex epsilon_Q2D = kroneckerdelta - potential*compute_quasi2D_PolarizabilityMatrixElement(q, g, g2, d); + + std::cout << "\nepsilon_2D(q = " << std::setprecision(10) << q(0) << "," << q(1) << "," << q(2) << ") = " << std::setprecision(30) << std::real(epsilon) << " + i" << std::imag(epsilon) << std::endl; + + std::cout << "\nepsilon_Q2D(d = " << d << ") = " << std::setprecision(17) << std::real(epsilon_Q2D) << " + i" << std::imag(epsilon_Q2D) << std::endl; + + return epsilon; + } + + return 0.0; +} + +/** + * Method to compute the inverse static dielectric function matrix at the specified momentum vector q. + * @return void +*/ +void ExcitonTB::computesingleInverseDielectricMatrix(std::string label) { + + auto start = high_resolution_clock::now(); + + if(mode == "realspace"){ + std::cout << "Real space dielectric function not implemented. Exiting." << std::endl; + + std::exit(0); + } + + arma::mat ReciprocalVectors = this->trunreciprocalLattice_; + uint nGs = ReciprocalVectors.n_rows; + std::string to_continue = "_"; + + std::string filename_dielectric = label + "_invepsilon.dat"; + FILE* textfile_dielectric = fopen(filename_dielectric.c_str(), "w"); + + if (textfile_dielectric == NULL){ + std::cout << "File for inverse of the dielectric matrix failed to open. Exiting" << std::endl; + exit(1); + } + + arma::cx_mat dielectric_matrix(nGs, nGs, arma::fill::zeros); + + arma::rowvec q_aux = this->q_; + + std::cout << "Computing inverse of dielectric matrix at momentum: q = " << this->q_ << std::endl; + arma::cx_mat auxvecsol(nGs,nGs,arma::fill::zeros); + arma::cx_mat auxvec(nGs,nGs,arma::fill::eye); + + arma::imat indecesg(nGs*(nGs+1)/2,2,arma::fill::zeros); + + int i = 0; + for (uint g = 0; g < nGs; g++){ + for (uint g2 = g; g2 < nGs; g2++){ + indecesg.row(i)(0) = g; + indecesg.row(i)(1) = g2; + i++; + } + } + + uint basisdim = system->basisdim; + vec auxEigVal(basisdim); + arma::cx_mat auxEigvec(basisdim, basisdim); + int nk = (int) this->nk_aux; + + if (this->eigveckqStack_.is_empty() && this->eigvalkqStack_.is_empty()) + { + this->eigveckqStack_ = arma::cx_cube(basisdim, basisdim, nk); + this->eigvalkqStack_ = arma::mat(basisdim, nk); + } + else if (((int) this->eigveckqStack_.n_slices != nk || (uint) this->eigvalkqStack_.n_rows != basisdim || (uint) this->eigvalkqStack_.n_cols != basisdim) || ((uint) this->eigvalKQStack_.n_rows != basisdim || (int) this->eigvalKQStack_.n_cols != nk)) + { + this->eigveckqStack_.reshape(basisdim, basisdim, nk); + this->eigvalkqStack_.reshape(basisdim, nk); + } + + std::cout << "Diagonalizing H(k+q) for every point k... " << std::flush; + for (uint i = 0; i < (uint) nk; i++) + { + arma::rowvec kq = this->kpoints_aux.row(i) + q_aux; + system->solveBands(kq, auxEigVal, auxEigvec); + auxEigvec = fixGlobalPhase(auxEigvec); + this->eigvalkqStack_.col(i) = auxEigVal; + this->eigveckqStack_.slice(i) = auxEigvec; + } + std::cout << "Done.\n" << std::flush; + + double d = this->d; + bool is_d_finite = std::abs(d) > 1E-4; + + #pragma omp parallel for + for (uint i = 0; i < nGs*(nGs+1)/2; i++){ + + int g = indecesg.row(i)(0); + int g2 = indecesg.row(i)(1); + + arma::rowvec G = ReciprocalVectors.row(g); + arma::rowvec G2 = ReciprocalVectors.row(g2); + + std::complex Chi = 0.0; + if (is_d_finite) { + Chi = compute_quasi2D_PolarizabilityMatrixElement(q_aux, G, G2, d); + } + else { + Chi = compute_2D_PolarizabilityMatrixElement(q_aux, G, G2); + } + + double potentialg = std::sqrt(coulomb_2D_FT(q_aux + G))*std::sqrt(coulomb_2D_FT(q_aux + G2)); + double kroneckerdelta = g == g2? 1 : 0; + + dielectric_matrix.row(g)(g2) = kroneckerdelta - potentialg*Chi; + dielectric_matrix.row(g2)(g) = kroneckerdelta - potentialg*std::conj(Chi); + } + + auxvecsol = arma::solve(dielectric_matrix,auxvec); + + for (unsigned int g = 0; g < nGs; g++){ + for (unsigned int g2 = 0; g2 < nGs; g2++){ + fprintf(textfile_dielectric, "%11.7lf%11.7lf", real(auxvecsol.row(g)(g2)), imag(auxvecsol.row(g)(g2))); + } + fprintf(textfile_dielectric, "\n"); + } + + fclose(textfile_dielectric); + + auto stop = high_resolution_clock::now(); + auto duration = duration_cast(stop - start); + + std::cout << "Done in " << duration.count()/1000.0 << " s.\n" << std::flush; +} + +/** + * Method to compute the regularization of the screened potential W_00(q) at q = 0 + * @details Computes numerically the head element of the inverse dielectric matrix at q = 0 + */ +void ExcitonTB::compute_ScreenedPotential_regularization(bool is_system_isotropic) +{ + std::cout << "\nComputing regularization for term W00(q = 0)... " << std::flush; + + // Takes the k vector of the BZ for the exciton closest to the origin + arma::mat k_mat_aux = system->kpoints; + sortVectors(k_mat_aux); + arma::rowvec q0 = this->percentage*k_mat_aux.row(1); + + + uint basisdim = this->system->basisdim; + uint nk = this->nk_aux; + + double q0_norm = arma::norm(q0); + arma::rowvec null_vector = {0., 0., 0.}; + + std::cout << "\nchosen percentage = " << this->percentage << " " <trunreciprocalLattice_; + + if (this->percentage == 0.0) { + this->W00_at_0_ = 0.0; + std::cout << "W00(q = 0) = " << this->W00_at_0_ << " eV " << std::endl; + return; + } + + if (this->potential_ == "coulomb"){ + + this->W00_at_0_ = 2 * ec * 1E10 / (2 * eps0 * q0_norm * system->unitCellArea); + + std::cout << "W00(q = 0) = " << this->W00_at_0_ << " eV " << std::endl; + + std::cout << "Done.\n" << std::endl; + return; + } + + if (this->potential_ == "keldysh"){ + + this->W00_at_0_ = (2 + this->r0*q0_norm) * ec * 1E10 / (2 * eps0 * q0_norm * system->unitCellArea); + + std::cout << "W00(q = 0) = " << this->W00_at_0_ << " eV " << std::endl; + + std::cout << "Done.\n" << std::endl; + return; + } + + // Calculates the head element of the dielectric matrix at q = q_0 -/*------------------------------------ Initializers ------------------------------------*/ + arma::cx_mat auxvecsol(nGs,nGs,arma::fill::zeros); + arma::cx_mat auxvec(nGs,nGs,arma::fill::eye); + arma::cx_mat dielectric_matrix(nGs, nGs, arma::fill::zeros); -/** - * Method to initialize the motif Fourier transform for all possible motif combination - * at a given kpoint. - * @param i Index of kpoint. - * @param cells Matrix of unit cells over which the motif FT is computed. - * @param potential Pointer to potential function. - * @return void - */ -void ExcitonTB::initializeMotifFT(int i, const arma::mat& cells, potptr potential){ - ftMotifStack.slice(i) = motifFTMatrix(system->meshBZ.row(i), cells, potential); -} + arma::imat indecesg(nGs*(nGs+1)/2,2,arma::fill::zeros); + + int i = 0; + for (uint g = 0; g < nGs; g++){ + for (uint g2 = g; g2 < nGs; g2++){ + indecesg.row(i)(0) = g; + indecesg.row(i)(1) = g2; + i++; + } + } + vec auxEigVal(basisdim); + arma::cx_mat auxEigvec(basisdim, basisdim); -/** - * Main method to compute all the relevant single-particle quantities (bands, eigenstates and fourier transforms), - * to compute the Bethe-Salpeter equation. - * @details It precomputes and saves the relevant data in the heap for later computations. - * @param triangular Boolean to specify whether the Hamiltonian matrices are triangular (default = false). - * @return void - */ -void ExcitonTB::initializeResultsH0(){ + if (this->eigveckqStack_.is_empty() && this->eigvalkqStack_.is_empty()) + { + this->eigveckqStack_ = arma::cx_cube(basisdim, basisdim, nk); + this->eigvalkqStack_ = arma::mat(basisdim, nk); + } + else if ((this->eigveckqStack_.n_slices != nk || (uint) this->eigvalkqStack_.n_rows != basisdim || (uint) this->eigvalkqStack_.n_cols != basisdim) || ((uint) this->eigvalKQStack_.n_rows != basisdim || this->eigvalKQStack_.n_cols != nk)) + { + this->eigveckqStack_.reshape(basisdim, basisdim, nk); + this->eigvalkqStack_.reshape(basisdim, nk); + } - int nTotalBands = bandList.n_elem; - double radius = arma::norm(system->bravaisLattice.row(0)) * cutoff_; - arma::mat cells = system_->truncateSupercell(ncell, radius); + std::cout << "Diagonalizing H(k+q) for every point k... " << std::flush; + for (uint i = 0; i < (uint) nk; i++) + { + arma::rowvec kq = this->kpoints_aux.row(i) + q0; + system->solveBands(kq, auxEigVal, auxEigvec); + auxEigvec = fixGlobalPhase(auxEigvec); + this->eigvalkqStack_.col(i) = auxEigVal; + this->eigveckqStack_.slice(i) = auxEigvec; + } - int nk = system->nk; - int natoms = system->natoms; - int basisdim = system->basisdim; + double d = this->d; + bool is_d_finite = std::abs(d) > 1E-4; + + #pragma omp parallel for + for (uint i = 0; i < nGs*(nGs+1)/2; i++){ - this->eigvecKStack_ = arma::cx_cube(basisdim, nTotalBands, nk); - this->eigvecKQStack_ = arma::cx_cube(basisdim, nTotalBands, nk); - this->eigvalKStack_ = arma::mat(nTotalBands, nk); - this->eigvalKQStack_ = arma::mat(nTotalBands, nk); - this->ftMotifStack = arma::cx_cube(natoms, natoms, system->meshBZ.n_rows); - this->ftMotifQ = arma::cx_mat(natoms, natoms); + int g = indecesg.row(i)(0); + int g2 = indecesg.row(i)(1); - vec auxEigVal(basisdim); - arma::cx_mat auxEigvec(basisdim, basisdim); - arma::cx_mat h; + arma::rowvec G = ReciprocalVectors.row(g); + arma::rowvec G2 = ReciprocalVectors.row(g2); + + std::complex Chi = 0.0; + if (is_d_finite) { + Chi = compute_quasi2D_PolarizabilityMatrixElement(q0, G, G2, d); + } + else { + Chi = compute_2D_PolarizabilityMatrixElement(q0, G, G2); + } - // Progress bar variables - int step = 1; - int displayNext = step; - int percent = 0; + double potentialg = std::sqrt(coulomb_2D_FT(q0 + G))*std::sqrt(coulomb_2D_FT(q0 + G2)); + double kroneckerdelta = g == g2? 1 : 0; + + dielectric_matrix.row(g)(g2) = kroneckerdelta - potentialg*Chi; + dielectric_matrix.row(g2)(g) = kroneckerdelta - potentialg*std::conj(Chi); + } - system_->calculateInverseReciprocalMatrix(); - std::complex imag(0, 1); + auxvecsol = arma::solve(dielectric_matrix,auxvec); - std::cout << "Diagonalizing H0 for all k points... " << std::flush; - for (int i = 0; i < nk; i++){ - arma::rowvec k = system->kpoints.row(i); - system->solveBands(k, auxEigVal, auxEigvec); + std::complex head_element = 1.0/auxvecsol.row(0)(0); - auxEigvec = fixGlobalPhase(auxEigvec); - eigvalKStack_.col(i) = auxEigVal(bandList); - eigvecKStack_.slice(i) = auxEigvec.cols(bandList); + double Re_head_element = std::real(head_element); + double Re_head_element_perp = Re_head_element; - if(arma::norm(Q) != 0){ - arma::rowvec kQ = system->kpoints.row(i) + Q; - system->solveBands(kQ, auxEigVal, auxEigvec); + if (!is_system_isotropic) { // If system is anisotropic, repeat the calculation for a vector perpendicular to q0 with same norm + arma::rowvec q0_perpendicular = {-q0(1), q0(0), 0}; + + std::cout << "Diagonalizing H(k+q) for every point k... " << std::flush; + for (uint i = 0; i < (uint) nk; i++) + { + arma::rowvec kq = this->kpoints_aux.row(i) + q0_perpendicular; + system->solveBands(kq, auxEigVal, auxEigvec); auxEigvec = fixGlobalPhase(auxEigvec); - eigvalKQStack_.col(i) = auxEigVal(bandList); - eigvecKQStack_.slice(i) = auxEigvec.cols(bandList); + this->eigvalkqStack_.col(i) = auxEigVal; + this->eigveckqStack_.slice(i) = auxEigvec; } - else{ - eigvecKQStack_.slice(i) = eigvecKStack.slice(i); - eigvalKQStack_.col(i) = eigvalKStack.col(i); - }; - - }; - std::cout << "Done" << std::endl; - if(this->mode == "realspace"){ - std::cout << "Computing lattice Fourier transform... " << std::flush; - potptr directPotential = selectPotential(this->potential_); #pragma omp parallel for - for (unsigned int i = 0; i < system->meshBZ.n_rows; i++){ - // BIGGEST BOTTLENECK OF THE CODE - initializeMotifFT(i, cells, directPotential); + for (uint i = 0; i < nGs*(nGs+1)/2; i++){ - /* AJU 24-11-23: Progress bar does not work properly with parallel for - Fix it or remove it direcly? */ - // percent = (100 * (i + 1)) / meshBZ.n_rows ; - // if (percent >= displayNext){ - // cout << "\r" << "[" << std::string(percent / 5, '|') << std::string(100 / 5 - percent / 5, ' ') << "]"; - // cout << percent << "%"; - // std::cout.flush(); - // displayNext += step; - // } - } - std::cout << "Done\n" << std::endl; - } + int g = indecesg.row(i)(0); + int g2 = indecesg.row(i)(1); - if(this->exchange){ - potptr exchangePotential = selectPotential(this->exchangePotential_); - this->ftMotifQ = motifFTMatrix(this->Q, cells, exchangePotential); - } -}; + arma::rowvec G = ReciprocalVectors.row(g); + arma::rowvec G2 = ReciprocalVectors.row(g2); -/** - * Routine to initialize the required variables to construct the Bethe-Salpeter Hamiltonian. - * @param triangular Boolean to specify whether the single-particle Hamiltonian matrices are triangular. - * @return void. - */ -void ExcitonTB::initializeHamiltonian(){ + std::complex Chi = 0.0; + if (is_d_finite) { + Chi = compute_quasi2D_PolarizabilityMatrixElement(q0_perpendicular, G, G2, d); + } + else { + Chi = compute_2D_PolarizabilityMatrixElement(q0_perpendicular, G, G2); + } - if(bands.empty()){ - throw std::invalid_argument("Error: Exciton object must have some bands"); - } - if(system->nk == 0){ - throw std::invalid_argument("Error: BZ mesh must be initialized first"); - } + double potentialg = std::sqrt(coulomb_2D_FT(q0_perpendicular + G))*std::sqrt(coulomb_2D_FT(q0_perpendicular + G2)); + double kroneckerdelta = g == g2? 1 : 0; + + dielectric_matrix.row(g)(g2) = kroneckerdelta - potentialg*Chi; + dielectric_matrix.row(g2)(g) = kroneckerdelta - potentialg*std::conj(Chi); + } - if (this->regularization_ < 1E-10){ - regularization_ = system->a; - } + auxvecsol = arma::solve(dielectric_matrix,auxvec); - this->excitonbasisdim_ = system->nk*valenceBands.n_elem*conductionBands.n_elem; - this->totalCells_ = pow(ncell*system->factor, system->ndim); + std::complex head_element = 1.0/auxvecsol.row(0)(0); - std::cout << "Initializing basis for BSE... " << std::flush; - initializeBasis(); - generateBandDictionary(); + Re_head_element_perp = std::real(head_element); + } - initializeResultsH0(); + this->W00_at_0_ = (2 + 0.5*(Re_head_element + Re_head_element_perp - 2)) * ec * 1E10 / (2 * eps0 * q0_norm * system->unitCellArea); + std::cout << "W00(q = 0) = " << this->W00_at_0_ << " eV." << std::endl; } /** * Method to initialize the BSE. * @details Calls the more general routine which allows * to specify a subset of the complete basis. - */ -void ExcitonTB::BShamiltonian(){ + */ +void ExcitonTB::BShamiltonian() +{ arma::imat basis = {}; BShamiltonian(basis); } @@ -892,8 +3444,25 @@ void ExcitonTB::BShamiltonian(const arma::imat& basis){ basisStates = basis; }; + if (((this->potential_ == "rpa" && this->Invepsilonmatrix_.is_zero()) || (this->exchangePotential_ == "rpa" && this->Invepsilonmatrix_.is_zero())) && this->mode == "reciprocalspace"){ + std::cout << "The Bethe-Salpeter Hamiltonian can not be initialized with the 'rpa' potential if the inverse of the dielectric matrix has not been computed. Terminating." << std::endl; + exit(0); + } + uint64_t basisDimBSE = basisStates.n_rows; std::cout << "BSE dimension: " << basisDimBSE << std::endl; + + if (this->mode == "reciprocalspace"){ + + uint nGs = system->truncateReciprocalSupercell(this->Gc_exciton_).n_rows; + + if ((uint) this->nReciprocalVectors != nGs) { + std::cout << "The number of G vectors to compute the exciton " << this->nReciprocalVectors << " does not match with the number of G vectors in the reciprocal sublattice " << nGs << " for the cutoff " << this->Gc_exciton_ << " angstrom^{-1}." << std::endl; + } + + this->compute_ScreenedPotential_regularization(this->isotropic); + } + std::cout << "this->nReciprocalVectors: " << this->nReciprocalVectors << std::endl; std::cout << "Initializing Bethe-Salpeter matrix... " << std::flush; HBS_ = arma::zeros(basisDimBSE, basisDimBSE); @@ -948,9 +3517,9 @@ void ExcitonTB::BShamiltonian(const arma::imat& basis){ else if (mode == "reciprocalspace"){ arma::rowvec k = system->kpoints.row(k_index); arma::rowvec k2 = system->kpoints.row(k2_index); - D = reciprocalInteractionTerm(coefsK, coefsK2, coefsKQ, coefsK2Q, k, k2, k, k2, this->nReciprocalVectors); + D = reciprocalInteractionTerm(coefsK, coefsK2, coefsKQ, coefsK2Q, k, k2, k + Q, k2 + Q, this->potential_, this->nReciprocalVectors); if(this->exchange){ - X = reciprocalInteractionTerm(coefsK2Q, coefsK2, coefsKQ, coefsK, k2 + Q, k2, k + Q, k, this->nReciprocalVectors); + X = reciprocalInteractionTerm(coefsK2Q, coefsK2, coefsKQ, coefsK, k2 + Q, k2, k + Q, k, this->exchangePotential_, this->nReciprocalVectors); } } @@ -1033,10 +3602,10 @@ double ExcitonTB::pairDensityOfStates(double energy, double delta) const { double dos = 0; for(int v = 0; v < (int)valenceBands.n_elem; v++){ for(int c = 0; c < (int)conductionBands.n_elem; c++){ - for(int i = 0; i < system->nk; i++){ + for(uint i = 0; i < system->nk; i++){ - arma::uword vband = bandToIndex.at(valenceBands(v)); // Unsigned integer - arma::uword cband = bandToIndex.at(conductionBands(c)); + uint vband = bandToIndex.at(valenceBands(v)); // Unsigned integer + uint cband = bandToIndex.at(conductionBands(c)); double stateEnergy = eigvalKStack.col(i)(cband) - eigvalKStack.col(i)(vband); dos += -PI*imag(rGreenF(energy, delta, stateEnergy)); @@ -1083,7 +3652,7 @@ cx_vec ExcitonTB::ehPairCoefs(double energy, const vec& gapEnergy, std::string s double eDiff; double currentEnergy = gapEnergy(0) - energy; - for(int n = 1; n < system->nk/2; n++){ + for(uint n = 1; n < system->nk/2; n++){ eDiff = gapEnergy(n) - energy; if(abs(eDiff) < abs(currentEnergy)){ @@ -1095,7 +3664,7 @@ cx_vec ExcitonTB::ehPairCoefs(double energy, const vec& gapEnergy, std::string s std::cout << "Selected k: " << system->kpoints(closestKindex) << "\t" << closestKindex << std::endl; std::cout << "Closest gap energy: " << gapEnergy(closestKindex) << std::endl; // By virtue of band symmetry, we expect n < nk/2 - double dispersion = PI/(16*system->a); + if(side == "left"){ coefs(closestKindex) = 1.; } @@ -1128,8 +3697,8 @@ double ExcitonTB::fermiGoldenRule(const ExcitonTB& targetExciton, // -------- Main loop (W initialization) -------- #pragma omp parallel for schedule(static, 1) collapse(2) - for (int i = 0; i < finalBasis.n_rows; i++){ - for (int j = 0; j < initialBasis.n_rows; j++){ + for (arma::uword i = 0; i < finalBasis.n_rows; i++){ + for (arma::uword j = 0; j < initialBasis.n_rows; j++){ arma::cx_vec coefsK, coefsK2, coefsKQ, coefsK2Q; @@ -1171,7 +3740,7 @@ double ExcitonTB::fermiGoldenRule(const ExcitonTB& targetExciton, else if (mode == "reciprocalspace"){ arma::rowvec k = system->kpoints.row(kf_index); arma::rowvec k2 = system->kpoints.row(ki_index); - D = reciprocalInteractionTerm(coefsK, coefsK2, coefsKQ, coefsK2Q, k, k2, k, k2, this->nReciprocalVectors); + D = reciprocalInteractionTerm(coefsK, coefsK2, coefsKQ, coefsK2Q, k, k2, k, k2, this->potential_, this->nReciprocalVectors); X = 0; } @@ -1181,7 +3750,7 @@ double ExcitonTB::fermiGoldenRule(const ExcitonTB& targetExciton, double delta = 2.4/(2*ncell); // Adjust delta depending on number of k points double rho = targetExciton.pairDensityOfStates(energy, delta); - cout << "DoS value: " << rho << endl; + std::cout << "DoS value: " << rho << endl; double hbar = 6.582119624E-16; // Units are eV*s transitionRate = 2*PI*std::norm(arma::cdot(finalState, W*initialState))*rho/hbar; @@ -1341,7 +3910,7 @@ double ExcitonTB::edgeFermiGoldenRule(const ExcitonTB& targetExciton, arma::cx_cube ftMotifStack = arma::cx_cube(natoms, natoms, system->kpoints.n_rows); #pragma omp parallel for collapse(2) - for(int i = 0; i < system->nk; i++){ + for(uint i = 0; i < system->nk; i++){ for(int fAtomIndex = 0; fAtomIndex < natoms; fAtomIndex++){ for(int sAtomIndex = fAtomIndex; sAtomIndex < natoms; sAtomIndex++){ ftMotifStack(fAtomIndex, sAtomIndex, i) = @@ -1355,7 +3924,7 @@ double ExcitonTB::edgeFermiGoldenRule(const ExcitonTB& targetExciton, // -------- Main loop (W initialization) -------- // #pragma omp parallel for - for (int i = 0; i < initialBasis.n_rows; i++){ + for (uint i = 0; i < initialBasis.n_rows; i++){ arma::cx_vec coefsK2, coefsK2Q; @@ -1382,7 +3951,7 @@ double ExcitonTB::edgeFermiGoldenRule(const ExcitonTB& targetExciton, } else if (mode == "reciprocalspace"){ arma::rowvec k2 = system->kpoints.row(ki_index); - D = reciprocalInteractionTerm(coefsK, coefsK2, coefsKQ, coefsK2Q, k, k2, k, k2, this->nReciprocalVectors); + D = reciprocalInteractionTerm(coefsK, coefsK2, coefsKQ, coefsK2Q, k, k2, k, k2, this->potential_, this->nReciprocalVectors); X = 0; } @@ -1391,7 +3960,7 @@ double ExcitonTB::edgeFermiGoldenRule(const ExcitonTB& targetExciton, double delta = 2.0/targetExciton.system->nk; // Adjust delta depending on number of k points double rho = targetExciton.pairDensityOfStates(energy, delta); - cout << "DoS value: " << rho << endl; + std::cout << "DoS value: " << rho << endl; double hbar = 6.582119624E-16; // Units are eV*s transitionRate = (ncell*system->a)*2*PI*std::norm(arma::dot(W, initialState))*rho/hbar; @@ -1405,37 +3974,349 @@ double ExcitonTB::edgeFermiGoldenRule(const ExcitonTB& targetExciton, * @return void */ void ExcitonTB::printInformation(){ - cout << std::left << std::setw(30) << "Number of cells: " << ncell << endl; - cout << std::left << std::setw(30) << "Valence bands:"; - for (int i = 0; i < valenceBands.n_elem; i++){ - cout << valenceBands(i) << " "; + std::cout << std::left << std::setw(30) << "Number of cells: " << ncell << endl; + std::cout << std::left << std::setw(30) << "Valence bands:"; + for (uint i = 0; i < valenceBands.n_elem; i++){ + std::cout << valenceBands(i) << " "; } - cout << endl; + std::cout << endl; - cout << std::left << std::setw(30) << "Conduction bands: "; - for (int i = 0; i < conductionBands.n_elem; i++){ - cout << conductionBands(i) << " "; + std::cout << std::left << std::setw(30) << "Conduction bands: "; + for (uint i = 0; i < conductionBands.n_elem; i++){ + std::cout << conductionBands(i) << " "; } - cout << "\n" << endl; + std::cout << "\n" << endl; - cout << std::left << std::setw(30) << "Gauge used: " << gauge << endl; - cout << std::left << std::setw(30) << "Calculation mode: " << mode << endl; + std::cout << std::left << std::setw(30) << "Gauge used: " << gauge << std::endl; + std::cout << std::left << std::setw(30) << "Calculation mode: " << mode << std::endl; if(mode == "reciprocalspace"){ - cout << std::left << std::setw(30) << "nG: " << nReciprocalVectors << endl; + std::cout << std::left << std::setw(30) << "Gc: " << Gc_exciton << " (angstrom^-1)" << std::endl; + std::cout << std::left << std::setw(30) << "nG: " << nReciprocalVectors << std::endl; } - cout << std::left << std::setw(30) << "Potential: " << potential_ << endl; + std::cout << std::left << std::setw(30) << "Potential: " << potential_ << std::endl; if(exchange){ - cout << std::left << std::setw(30) << "Exchange: " << (exchange ? "True" : "False") << endl; - cout << std::left << std::setw(30) << "Exchange potential: " << exchangePotential_ << endl; + std::cout << std::left << std::setw(30) << "Exchange: " << (exchange ? "True" : "False") << std::endl; + std::cout << std::left << std::setw(30) << "Exchange potential: " << exchangePotential_ << std::endl; } + std::cout << std::left << std::setw(30) << "Dielectric constant of embedding medium: " << eps_m << std::endl; + std::cout << std::left << std::setw(30) << "Dielectric constant of substrate: " << eps_s << std::endl; if(arma::norm(Q) > 1E-7){ - cout << std::left << std::setw(30) << "Q: "; + std::cout << std::left << std::setw(30) << "Q: "; for (auto qi : Q){ - cout << qi << " "; + std::cout << qi << " "; + } + std::cout << std::endl; + } + std::cout << std::left << std::setw(30) << "Scissor cut: " << scissor_ << std::endl; + + if (this->isscreeningset == true){ + std::cout << std::left << std::setw(40) << "\nNumber of valence bands included: " << this->nvalencebands_ << std::endl; + std::cout << std::left << std::setw(40) << "Number of conduction bands included: " << this->nconductionbands_ << std::endl; + std::cout << std::left << std::setw(40) << "Gcutoff: " << this->Gcutoff_ << std::endl; + if (this->function_ == "dielectric" || this->function_ == "polarizability"){ + if (this->mode == "reciprocalspace"){ + arma::rowvec vector(this->trunreciprocalLattice_.row(this->Gs_(0))); + arma::rowvec vectorprime(this->trunreciprocalLattice_.row(this->Gs_(1))); + + std::cout << std::left << std::setw(0) << "Selected G(" << std::setw(0) << this->Gs_(0) << "): " << vector(0) << " " << vector(1) << " " << vector(2) << std::endl; + std::cout << std::left << std::setw(0) << "Selected G'(" << std::setw(0) << this->Gs_(1) << "): " << vectorprime(0) << " " << vectorprime(1) << " " << vectorprime(2) << std::endl; + } + + if (this->mode == "realspace"){ + std::cout << "Numerical screening in real space not implemented. Terminating." << std::endl; + exit(0); + } + + } else if (this->function_ == "none" || this->function_ == "inversedielectric") { + std::cout << std::left << std::setw(40) << "Number of reciprocal lattice vectors: " << this->nGs << std::endl; + } + } +} + +/** + * Method to print reciprocal lattice + * @return void + */ +void ExcitonTB::printReciprocalLattice() { + double cutoff = this->Gc_exciton; + uint nGs_total = this->trunreciprocalLattice_.n_rows; + + std::cout << "Reciprocal lattice vectors within cutoff |G| <= " << cutoff << " (angstrom^-1):" << std::endl; + + for (uint i = 0; i < nGs_total; i++) + { + arma::rowvec G = this->trunreciprocalLattice_.row(i); + + if (arma::norm(G) <= cutoff) { + std::cout << "G = G(" << i << ") = (" << G(0) << ", " << G(1) << ", " << G(2) << ") |G| = " << arma::norm(G) << std::endl; + } else { + return; + } + } +} + +/** + * Method to write the BZ mesh to a file. + * @return void +*/ +void ExcitonTB::writeBZtofile() const { + std::string filename_k_points = "kgrid_" + std::to_string(this->ncell) + ".dat"; + + std::ofstream k_points_file; + + k_points_file.open(filename_k_points); + + if (!k_points_file.is_open()) { // check if the file was opened successfully + std::cerr << "Error opening file\n"; + std::cerr << errno << "\n"; + } + + + for(unsigned int i = 0; i < this->ncell*this->ncell; i++){ + auto k = this->system->kpoints.row(i); + k_points_file << k(0) << " " << k(1) << " " << k(2) << std::endl; + } + + k_points_file.close(); +} + +/* Method to print information of the inverse of the dielectric matrix into a file. + * @return void + */ +void ExcitonTB::writeInverseDielectricMatrix(std::string filename_dielectric) { + + FILE* textfile = fopen(filename_dielectric.c_str(), "w"); + + if (textfile == NULL){ + std::cout << "File for inverse of the dielectric matrix failed to open. Exiting" << std::endl; + exit(0); + } + + std::cout << "Writing inverse of dielectric matrix fo file: " << filename_dielectric << std::endl; + + if (this->mode == "realspace"){ + std::cout << "Real space implementation ongoing. Terminating." << std::endl; + exit(0); + } + + if (this->mode == "reciprocalspace"){ + + uint ngs = this->epsilonmatrix_.slice(0).n_rows; // The number of G vectors can in general be different from the number of generated G vectors + uint nqs = this->epsilonmatrix_.n_slices; // The number of q points can in general be different from the size of the BZ mesh + + if (ngs == 0 || nqs == 0){ + std::cout << "Dielectric matrix was not computed. Exiting." << std::endl; + exit(0); + } + + if (this->Invepsilonmatrix_.is_empty()) { + + std::cout << "\nInverse dielectric matrix was not computed." << std::endl; + + try{ + this->Invepsilonmatrix_ = arma::cx_cube(ngs,ngs,nqs,arma::fill::zeros); + + this->invertDielectricMatrix(); + + } catch(const std::exception& e){ + std::cerr << e.what() << std::endl; + } + } + + + for(uint i = 0; i < nqs; i++){ + for (uint g = 0; g < ngs; g++){ + for (uint g2 = 0; g2 < ngs; g2++){ + std::complex aux = this->Invepsilonmatrix_.slice(i).at(g,g2); + fprintf(textfile, "%11.7lf%11.7lf", real(aux), imag(aux)); + } + fprintf(textfile, "\n"); + } + } + } + + fclose(textfile); +} + +/* Method to print information of the inverse of the dielectric matrix into a file. + * @return void + */ +void ExcitonTB::writeDielectricMatrix(std::string filename_dielectric) const +{ + + FILE *textfile = fopen(filename_dielectric.c_str(), "w"); + + if (textfile == NULL) + { + std::cout << "File for the dielectric matrix failed to open. Exiting" << std::endl; + exit(0); + } + + std::cout << "Writing inverse of dielectric matrix fo file: " << filename_dielectric << std::endl; + + if (this->mode == "realspace") + { + std::cout << "Real space implementation ongoing. Terminating." << std::endl; + exit(0); + } + + if (this->mode == "reciprocalspace") + { + uint ngs = this->epsilonmatrix_.slice(0).n_rows; // The number of G vectors can in general be different from the number of generated G vectors + uint nqs = this->epsilonmatrix_.n_slices; // The number of q points can in general be different from the size of the BZ mesh + + for (unsigned int i = 0; i < nqs; i++) + { + for (unsigned int g = 0; g < ngs; g++) + { + for (unsigned int g2 = 0; g2 < ngs; g2++) + { + std::complex aux = this->epsilonmatrix_.slice(i).at(g, g2); + fprintf(textfile, "%11.7lf%11.7lf", real(aux), imag(aux)); + } + fprintf(textfile, "\n"); + } + } + } + + fclose(textfile); +} + +/* Method to print information of the polarizability matrix into a file. + * @return void + */ +void ExcitonTB::writePolarizabilityMatrix(std::string filename_dielectric) const { + + FILE* textfile = fopen(filename_dielectric.c_str(), "w"); + + if (textfile == NULL){ + std::cout << "File for polarizability matrix failed to open. Exiting." << std::endl; + exit(0); + } + + std::cout << "Writing polarizability matrix fo file: " << filename_dielectric << std::endl; + + if (this->mode == "realspace"){ + std::cout << "Real space implementation ongoing. Terminating." << std::endl; + exit(0); + } + + if (this->mode == "reciprocalspace"){ + uint ngs = this->trunreciprocalLattice_.n_rows; // The number of G vectors can in general be different from the number of generated G vectors + uint nqs = this->Chimatrix_.n_slices; // The number of q points can in general be different from the size of the BZ mesh + std::cout << "ngs = " << ngs << std::endl; + for(unsigned int i = 0; i < nqs; i++){ + for (unsigned int g = 0; g < ngs; g++){ + for (unsigned int g2 = 0; g2 < ngs; g2++){ + std::complex aux = this->Chimatrix_.slice(i).at(g,g2); + fprintf(textfile, "%11.7lf%11.7lf", real(aux), imag(aux)); + } + fprintf(textfile, "\n"); + } } - cout << endl; + std::cout << "Polarizability_00 = " << this->Chimatrix_.slice(0).at(0,0) << std::endl; } - cout << std::left << std::setw(30) << "Scissor cut: " << scissor_ << endl; + + fclose(textfile); } +/* Method to read the inverse of the dielectric matrix from a pre-existent one stored in a file. + * @return void + */ +void ExcitonTB::readInverseDielectricMatrix(std::string filename_screening) { + + std::complex imag(0,1); + + std::ifstream file; + + file.open(filename_screening); + + if (!file.is_open()){ + std::cout << "File for inverse of the dielectric matrix failed to open or does not exist. Terminating." << std::endl; + exit(0); + } + + std::cout << "Reading inverse of dielectric matrix from file: " << filename_screening << std::endl; + + if (this->mode == "realspace"){ + std::cout << "Exciton computed with real space screening not implemented. Terminating." << std::endl; + exit(0); + } + + if (this->mode == "reciprocalspace"){ + + uint ngs = this->trunreciprocalLattice_.n_rows; + int nqs = system->nk; + int line_counter = 0; + uint column_counter = 0; + int k_counter = 0; + std::string line; + + std::string fl; + std::getline(file, fl); // get first line + + std::istringstream iss(fl); + double m_element; + while(iss >> m_element) { + column_counter++; + } + + if (ngs != column_counter/2){ + std::cout << "The number of reciprocal vectors read from file and from the configuration do not coincide! Terminating." << std::endl; + exit(0); + } + + file.seekg(0); // go back to the beginning of the file + + while (std::getline(file, line)) { + ++line_counter; + } + + file.clear(); // clear the error state + + int read_nqs = line_counter/ngs; + + if (nqs != read_nqs) { + std::cout << "The number of k points read from data file (" + std::to_string(read_nqs) + ") and from the exciton configuration file (" + std::to_string(nqs) + ") do not coincide!\n The exciton can not be computed with the provided screening data file. Terminating." << std::endl; + exit(0); + } + + file.seekg(0); + + if (this->Invepsilonmatrix_.is_empty()) { + this->Invepsilonmatrix_ = arma::cx_cube(ngs,ngs,nqs,arma::fill::zeros); + } else { + + this->Invepsilonmatrix_.reshape(ngs,ngs,nqs); + } + + line_counter = 0; + while (std::getline(file, line)) { + std::istringstream ss(line); + double Re_part = 0; + double Im_part = 0; + double aux; + column_counter = 0; + + while(ss >> aux) { + if (column_counter%2 == 0) { + Re_part = aux; + } else { + Im_part = aux; + this->Invepsilonmatrix_.slice(k_counter)(line_counter%ngs, (column_counter - 1)/2) = Re_part + imag*Im_part; + } + column_counter++; + } + + ++line_counter; + if (line_counter%ngs == 0){ + k_counter++; + } + } + } + + std::cout << "Inverse of dielectric matrix read from file with success." << std::endl; + + file.close(); +} } diff --git a/src/Lattice.cpp b/src/Lattice.cpp index 852dd99..c587d64 100755 --- a/src/Lattice.cpp +++ b/src/Lattice.cpp @@ -2,6 +2,26 @@ #include #include "xatu/Lattice.hpp" +/** + *Method to sort rows in a matrix by norm + *@return void +*/ +void sortVectors(arma::mat& vectors){ + + std::vector vecs; + + for (int i = 0; i < (int)vectors.n_rows; ++i) + vecs.push_back(vectors.row(i)); + + std::sort(vecs.begin(), vecs.end(), [](const arma::rowvec & a, const arma::rowvec & b){ return arma::norm(a) < arma::norm(b); }); + + for (int i = 0; i < (int)vectors.n_rows; ++i){ + vectors.row(i)(0) = vecs[i][0]; + vectors.row(i)(1) = vecs[i][1]; + vectors.row(i)(2) = vecs[i][2]; + } +} + namespace xatu { /** @@ -311,6 +331,48 @@ arma::mat Lattice::generateCombinations(int nvalues, int ndim, bool centered){ return combinations; } +/** + * Method to generate a list with combinations of primitive reciprocal lattice vectors, ordered in a specific way (they are sorted at another instance). + * @details Each row of the list stores the integers which correspond + * to the coefficients of the linear combinations of Bravais basis vectors. + * @param nvalues Number of cells in one direction. + * @param ndim Dimension of the system. + * @returns List of cell combinations. +*/ +arma::imat Lattice::generateCombinationsGcutoff(double Gc, int ndim){ + + // Gcutoff is the norm of a certain G-vector, and include all G-vectors such that |G| <= Gcutoff + + double normG1 = arma::norm(reciprocalLattice.row(0)); + double normG2 = arma::norm(reciprocalLattice.row(1)); + //double normG3 = arma::norm(reciprocalLattice.row(2)); + + //For now implements only 2D systems + int n_max = 4*std::ceil(Gc/normG1); // scaling factor to ensure that all the G-vectos with |G| <= Gc are included + int m_max = 4*std::ceil(Gc/normG2); + + int ncombinations = (2*n_max + 1)*(2*m_max + 1); + + arma::imat combinations(ncombinations, ndim); + + //This piece of code generates all the combinations of (n,m) pairs to generate any reciprocal lattice vector n*G1 + m*G2 with norm smaller than or equal to Gc + int i_row = 0; + + for (int n = -n_max; n <= n_max; n++) + { + for (int m = -m_max; m <= m_max; m++) + { + combinations.row(i_row)(0) = n; + combinations.row(i_row)(1) = m; + i_row++; + } + } + + + return combinations; +} + + /** * Method to generate a list of cells within a sphere of specified radius. * @param ncell List of cells along one axis. @@ -342,13 +404,12 @@ arma::mat Lattice::truncateSupercell(int ncell, double radius){ /** * Method to generate a list of reciprocal cells contained within a sphere of specified radius. - * @param ncell List of cells in one direction. * @param radius Radius of the cutoff sphere. - * @returns List of reciprocal cells in cartesian coordinates. + * @returns List of (sorted) reciprocal cells in cartesian coordinates. */ -arma::mat Lattice::truncateReciprocalSupercell(int ncell, double radius){ +arma::mat Lattice::truncateReciprocalSupercell(double radius){ - arma::mat combinations = generateCombinations(ncell, ndim, true); + arma::imat combinations = generateCombinationsGcutoff(radius, ndim); std::vector cells_vector; for (int i = 0; i < combinations.n_rows; i++){ arma::rowvec lattice_vector = arma::zeros(3); @@ -366,6 +427,8 @@ arma::mat Lattice::truncateReciprocalSupercell(int ncell, double radius){ cells.row(i) = cells_vector[i]; } + sortVectors(cells); + return cells; } @@ -389,5 +452,4 @@ arma::rowvec Lattice::rotateC3(const arma::rowvec& position){ }; -} - +} \ No newline at end of file diff --git a/src/ScreeningConfiguration.cpp b/src/ScreeningConfiguration.cpp new file mode 100644 index 0000000..24b1ea8 --- /dev/null +++ b/src/ScreeningConfiguration.cpp @@ -0,0 +1,125 @@ +#include +#include +#include "xatu/ScreeningConfiguration.hpp" + +namespace xatu { + +/** + * Default constructor. + * @details Throws an error if called. Class must be constructed providing a filename with the configuration. + */ +ScreeningConfiguration::ScreeningConfiguration(){ + throw std::invalid_argument("Error: ScreeningConfiguration must be invoked with one argument (filename)"); +}; + +/** + * File constructor. + * @details ScreeningConfiguration must be initialized always with this constructor. + * Upon call, the exciton configuration file is fully parsed and the information extracted. + * @param filename Name of file with the exciton configuration. + */ +ScreeningConfiguration::ScreeningConfiguration(std::string filename) : ConfigurationBase(filename){ + this->expectedArguments = {"function","valence.bands","conduction.bands","ncell_aux","spin","gcutoff"}; + parseContent(); + checkArguments(); + checkContentCoherence(); +} + +/** + * Method to parse the exciton configuration from its file. + * @details This method extracts all information from the configuration file and + * stores it with the adequate format in the information struct. + */ +void ScreeningConfiguration::parseContent(){ + extractArguments(); + extractRawContent(); + + if (contents.empty()){ + throw std::logic_error("File contents must be extracted first"); + } + for(const auto& arg : foundArguments){ + auto content = contents[arg]; + + if (content.size() == 0){ + continue; + } + else if(content.size() != 1){ + throw std::logic_error("Expected only one line per field"); + } + else if(arg == "valence.bands"){ + screeningInfo.nvbands = parseScalar(content[0]); + } + else if(arg == "conduction.bands"){ + screeningInfo.ncbands = parseScalar(content[0]); + } + else if(arg == "vectors"){ + std::vector gs = parseLine(content[0]); + screeningInfo.Gs(0) = gs[0]; + screeningInfo.Gs(1) = gs[1]; + } + else if(arg == "momentum"){ + std::vector momentum = parseLine(content[0]); + screeningInfo.q = arma::rowvec(momentum); + } + else if(arg == "function"){ + screeningInfo.function = parseWord(content[0]); + } + else if(arg == "gcutoff"){ + screeningInfo.Gcutoff = parseScalar(content[0]); + } + else if(arg == "spin"){ + std::string spin_string = parseWord(content[0]); + if (spin_string == "false") { + screeningInfo.spin = false; + } else if (spin_string == "true") { + screeningInfo.spin = true; + } else { + std::cout << "Option for spin not recognized, skipping block..." << std::endl; + } + } else if(arg == "ncell_aux"){ + screeningInfo.ncell_aux = parseScalar(content[0]); + } else if(arg == "thickness"){ + screeningInfo.d = parseScalar(content[0]); + } else if(arg == "isotropic"){ + std::string isotropic_string = parseWord(content[0]); + + if (isotropic_string == "false") { + screeningInfo.isotropic = false; + } else if (isotropic_string == "true") { + screeningInfo.isotropic = true; + } else { + std::cout << "Option for isotropic not recognized, skipping block..." << std::endl; + } + } + else{ + std::cout << "Unexpected argument: " << arg << ", skipping block..." << std::endl; + } + } +}; + +/** + * Method to check whether the information extracted from the configuration file is + * consistent and well-defined. + */ +void ScreeningConfiguration::checkContentCoherence(){ + if(screeningInfo.nvbands <= 0){ + throw std::logic_error("'nvbands' must be a positive number"); + }; + if(screeningInfo.ncbands <= 0){ + throw std::logic_error("'ncbands' must be a positive number"); + } + if(screeningInfo.function != "dielectric" && screeningInfo.function != "polarizability" && screeningInfo.function != "inversedielectric" && screeningInfo.function != "exciton"){ + throw std::logic_error("'function' must be 'dielectric', 'polarizability', 'inversedielectric' or 'exciton'"); + } + if(screeningInfo.Gs(0) < 0 || screeningInfo.Gs(1) < 0){ + throw std::invalid_argument("The indeces of the vectors must be zero or a positive integer."); + } + if(screeningInfo.ncell_aux < 1){ + throw std::invalid_argument("The number of points in the coarser BZ mesh in each direction, ncell_aux, has to be positive."); + } + if(screeningInfo.d < 0){ + throw std::invalid_argument("The thickness of the material must not be negative."); + } +}; + +} \ No newline at end of file diff --git a/src/SystemTB.cpp b/src/SystemTB.cpp index 9a37e57..ddd790c 100755 --- a/src/SystemTB.cpp +++ b/src/SystemTB.cpp @@ -127,7 +127,7 @@ void SystemTB::solveBands(arma::rowvec& k, arma::vec& eigval, arma::cx_mat& eigv /** * Method to orthogonalize the basis. * @details This method acts directly over the eigenstates of the system, giving us - * their coefficients if their were written in an orthonormal basis. The technique used + * their coefficients if they were written in an orthonormal basis. The technique used * is Lowdin orthogonalization. * @param k kpoint of eigenvectors to orthonormalize. * @param hamiltonian Matrix of eigenstates. diff --git a/src/Wannier90Configuration.cpp b/src/Wannier90Configuration.cpp index 648ab4f..f14251a 100644 --- a/src/Wannier90Configuration.cpp +++ b/src/Wannier90Configuration.cpp @@ -116,7 +116,7 @@ namespace xatu { iss.clear(); } } - // fockMatrices.slice(i) /= Degen(i); // correcting double-counted neighbors + fockMatrices.slice(i) /= Degen(i); // correcting double-counted neighbors std::getline(m_file, line); } diff --git a/src/skubo_w.f90 b/src/skubo_w.f90 index c75b1f2..081c7c5 100644 --- a/src/skubo_w.f90 +++ b/src/skubo_w.f90 @@ -455,7 +455,18 @@ subroutine get_kubo_parameters(w0,wrange,nw,eta,type_broad, & character(100) file_name_ex !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! -open(10,file='kubo_w.in') +! Try to open the file only if it exists +open(unit=10, file='../kubo_w.in', status='old', iostat=iostat_var) + +if (iostat_var /= 0) then + print *, "Error: File 'kubo_w.in' does not exist or could not be opened." + ! Handle the error, e.g., by stopping the program or taking other actions + stop +else + print *, "File 'kubo_w.in' opened successfully." +end if + + ! Close the file if it was opened read(10,*) read(10,*) w0 read(10,*) @@ -469,6 +480,9 @@ subroutine get_kubo_parameters(w0,wrange,nw,eta,type_broad, & read(10,*) read(10,*) file_name_sp read(10,*) file_name_ex +print *, "Writing absorption spectrum to files:" +print *, file_name_sp +print *, file_name_ex close(10) return diff --git a/test/tests.cpp b/test/tests.cpp index 934c905..01cb73d 100644 --- a/test/tests.cpp +++ b/test/tests.cpp @@ -281,6 +281,41 @@ TEST(FileParsing, ExcitonfileParsingAnisotropic){ EXPECT_EQ(xatu::array2hash(config.excitonInfo.Q), 0); } + +TEST(FileParsing, ScreeningParsing){ + + std::cout.clear(); + std::cout << std::setw(40) << std::left << "Testing screening file parsing... "; + std::cout.setstate(std::ios_base::failbit); + + std::string screeningfile = "../examples/screeningconfig/hBN_DFT_screening.txt"; + xatu::ScreeningConfiguration config = xatu::ScreeningConfiguration(screeningfile); + + std::string expectedfunction = "dielectric"; + int expectedNcell_aux = 10; + int expected_valence_bands = 6; + int expected_conduction_bands = 63; + bool expectedspin = false; + bool expectedisotropic = true; + double expectedGcutoff = 3.0; + arma::ivec expectedvectors = arma::ivec({0, 0}); + arma::rowvec expectedmomentum = {0.2, 0., 0.}; + + EXPECT_EQ(config.screeningInfo.ncell_aux, expectedNcell_aux); + EXPECT_EQ(config.screeningInfo.nvbands, expected_valence_bands); + EXPECT_EQ(config.screeningInfo.ncbands, expected_conduction_bands); + EXPECT_EQ(config.screeningInfo.spin, expectedspin); + EXPECT_EQ(config.screeningInfo.isotropic, expectedisotropic); + EXPECT_EQ(config.screeningInfo.Gcutoff, expectedGcutoff); + EXPECT_EQ(config.screeningInfo.Gs(0), expectedvectors(0)); + EXPECT_EQ(config.screeningInfo.Gs(1), expectedvectors(1)); + EXPECT_EQ(config.screeningInfo.q(0), expectedmomentum(0)); + EXPECT_EQ(config.screeningInfo.q(1), expectedmomentum(1)); + EXPECT_EQ(config.screeningInfo.q(2), expectedmomentum(2)); + + std::cout.clear(); + std::cout << std::setw(40) << "\033[1;32m Success \033[0m" << std::endl; +} TEST(hBNTest, FullDiagonalization){ @@ -383,7 +418,7 @@ TEST(hBNTest, ReciprocalSpaceMethod){ xatu::ExcitonTB exciton = xatu::ExcitonTB(config, ncell, 1, 0, {1, 1, 10}); exciton.setMode("reciprocalspace"); - exciton.setReciprocalVectors(5); + exciton.setGcutoff(3.0); exciton.brillouinZoneMesh(ncell); exciton.initializeHamiltonian(); @@ -392,9 +427,9 @@ TEST(hBNTest, ReciprocalSpaceMethod){ auto energies = xatu::detectDegeneracies(results->eigval, nstates, 6); - std::vector> expectedEnergies = {{6.234291, 1}, - {6.236636, 1}, - {6.731819, 1}}; + std::vector> expectedEnergies = {{6.200045075, 1}, + {6.300352, 1}, + {6.832558, 1}}; for(uint i = 0; i < energies.size(); i++){ EXPECT_NEAR(energies[i][0], expectedEnergies[i][0], 1E-4); EXPECT_EQ(energies[i][1], expectedEnergies[i][1]); @@ -1042,6 +1077,146 @@ TEST(MoS2Test, Conductivity){ } +TEST(ScreeningTest, hBNDFTScreening){ + + std::cout.clear(); + std::cout << std::setw(40) << std::left << "Testing DFT hBN screening (polarizability, direct dielectric matrix, and inverse dielectric matrix)... "; + std::cout.setstate(std::ios_base::failbit); + + std::string modelfile = "../examples/material_models/DFT/hBN_base_HSE06.outp"; + xatu::CRYSTALConfiguration config = xatu::CRYSTALConfiguration(modelfile, 100); + + std::unique_ptr systemConfig = std::unique_ptr(new xatu::CRYSTALConfiguration(modelfile, 100)); + + int ncell = 10; + double Gcutoff = 3.0; + double d = 3.33; + double percentage = 0.5; + int nstates = 2; + uint nvbands = 6; + uint ncbands = 63; + uint ncell_aux = 10; + bool spinfull = false; + bool isotropic = true; + + xatu::ExcitonTB exciton = xatu::ExcitonTB(*systemConfig, ncell, 1, 0, {1., 1., 10.}, {0., 0., 0.}, ncell_aux, nvbands, ncbands, Gcutoff, Gcutoff, d, spinfull, isotropic); + + exciton.system->setAU(true); + exciton.brillouinZoneMesh(ncell); + exciton.initializeHamiltonian(); + + std::complex expectedepsilon = 2.001461924; + + std::complex epsilon = exciton.computesingleDielectricFunctionMatrixElement(); + + EXPECT_NEAR(std::real(epsilon), std::real(expectedepsilon), 1E-4); + + std::cout.clear(); + std::cout << std::setw(40) << "\033[1;32m Success \033[0m" << std::endl; +} + +TEST(ScreeningTest, hBNDFTExciton){ + + std::cout.clear(); + std::cout << std::setw(40) << std::left << "Testing DFT hBN exciton calculation with screening... "; + std::cout.setstate(std::ios_base::failbit); + + std::string modelfile = "../examples/material_models/DFT/hBN_base_HSE06.outp"; + std::unique_ptr systemConfig = std::unique_ptr(new xatu::CRYSTALConfiguration(modelfile, 100)); + std::string dielectric_matrix_path = "../data/hBN_DFT_HSE06_Q2D_BZ_N20_Gc_5_1_invepsilon.dat"; + + int ncell = 20; + double Gcutoff = 5.1; + double d = 3.33; + double percentage = 0.5; + int nstates = 2; + uint nvbands = 6; + uint ncbands = 63; + uint ncell_aux = 10; + bool spinfull = false; + bool isotropic = true; + int holeIndex = 1; + arma::rowvec holeCell = {0, 0, 0}; + + xatu::ExcitonTB exciton = xatu::ExcitonTB(*systemConfig, ncell, 1, 0, {1., 1., 10.}, {0., 0., 0.}, ncell_aux, nvbands, ncbands, Gcutoff, Gcutoff, d, spinfull, isotropic); + + exciton.system->setAU(true); + exciton.setPercentage(percentage); + + exciton.brillouinZoneMesh(ncell); + exciton.readInverseDielectricMatrix(dielectric_matrix_path); + exciton.initializeHamiltonian(); + + exciton.BShamiltonian(); + + auto results = exciton.diagonalize("diag", nstates); + + auto energies = xatu::detectDegeneracies(results->eigval, nstates, 6); + + std::vector> expectedEnergies = {{3.696992, 1}, + {3.730510, 1}}; + + for(uint i = 0; i < energies.size(); i++){ + EXPECT_NEAR(energies[i][0], expectedEnergies[i][0], 1E-4); + EXPECT_EQ(energies[i][1], expectedEnergies[i][1]); + } + + std::cout.clear(); + std::cout << std::setw(40) << "\033[1;32m Success \033[0m" << std::endl; + + // Check reciprocal w.f. + int nbandsCombinations = exciton.conductionBands.n_elem * exciton.valenceBands.n_elem; + arma::cx_vec kwf = arma::zeros(exciton.system->kpoints.n_rows); + for (int n = 0; n < nstates; n++){ + arma::cx_vec statecoefs = results->eigvec.col(n); + for (int i = 0; i < exciton.system->kpoints.n_rows; i++){ + double coef = 0; + for(int nband = 0; nband < nbandsCombinations; nband++){ + coef += abs(statecoefs(nbandsCombinations*i + nband))* + abs(statecoefs(nbandsCombinations*i + nband)); + }; + coef /= arma::norm(exciton.system->kpoints.row(1) - exciton.system->kpoints.row(0)); // L2 norm instead of l2 + kwf(i) += coef; + }; + } + + double kwfHash = xatu::array2hash(kwf); + double expectedKwfHash = 1.086489570724429; + if(std::abs(kwfHash-expectedKwfHash) < 1E-5){ + std::cout << "\033[1;32m Reciprocal w.f. correct \033[0m" << std::endl; + } + std::cout << std::setw(40) << "kwfHash: " << kwfHash << std::endl; + + // Check realspace w.f. + arma::rowvec holePosition = exciton.system->motif.row(holeIndex).subvec(0, 2) + holeCell; + std::cout << "Hole position: " << holePosition << std::endl; + double radius = arma::norm(exciton.system->bravaisLattice.row(0)) * exciton.ncell; + arma::mat cellCombinations = exciton.system->truncateSupercell(exciton.ncell, 2); + arma::vec rswf = arma::zeros(cellCombinations.n_rows*exciton.system->motif.n_rows); + + // Compute probabilities + for(int n = 0; n < nstates; n++){ + int it = 0; + arma::cx_vec statecoefs = results->eigvec.col(n); + for(unsigned int cellIndex = 0; cellIndex < cellCombinations.n_rows; cellIndex++){ + arma::rowvec cell = cellCombinations.row(cellIndex); + for (unsigned int atomIndex = 0; atomIndex < exciton.system->motif.n_rows; atomIndex++){ + rswf(it) += results->realSpaceWavefunction(statecoefs, atomIndex, holeIndex, cell, holeCell); + it++; + } + } + } + + double rswfHash = xatu::array2hash(rswf); + double expectedRSwfHash = 91.4518564389955063; + if(std::abs(rswfHash-expectedRSwfHash) < 1E-5){ + std::cout << "\033[1;32m Real space w.f. correct \033[0m" << std::endl; + } + std::cout << std::setw(40) << "rswfHash: " << rswfHash << std::endl; + std::cout.clear(); + std::cout << std::setw(40) << "\033[1;32m Success \033[0m" << std::endl; + +} int main(int argc, char **argv) { ::testing::InitGoogleTest(&argc, argv);