-
Notifications
You must be signed in to change notification settings - Fork 28
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
- Loading branch information
Showing
3 changed files
with
255 additions
and
5 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
246 changes: 246 additions & 0 deletions
246
include/dca/phys/models/analytic_hamiltonians/complex_square_lattice.hpp
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,246 @@ | ||
| // Copyright (C) 2018 ETH Zurich | ||
| // Copyright (C) 2018 UT-Battelle, LLC | ||
| // All rights reserved. | ||
| // | ||
| // See LICENSE for terms of usage. | ||
| // See CITATION.md for citation guidelines, if DCA++ is used for scientific publications. | ||
| // | ||
| // Author: Peter Staar (taa@zurich.ibm.com) | ||
| // Urs R. Haehner (haehneru@itp.phys.ethz.ch) | ||
| // | ||
| // Square lattice. | ||
|
|
||
| #ifndef DCA_PHYS_MODELS_ANALYTIC_HAMILTONIANS_COMPLEX_SQUARE_LATTICE_HPP | ||
| #define DCA_PHYS_MODELS_ANALYTIC_HAMILTONIANS_COMPLEX_SQUARE_LATTICE_HPP | ||
|
|
||
| #include <stdexcept> | ||
| #include <utility> | ||
| #include <vector> | ||
|
|
||
| #include "dca/function/domains.hpp" | ||
| #include "dca/function/function.hpp" | ||
| #include "dca/linalg/matrix.hpp" | ||
| #include "dca/phys/domains/cluster/cluster_definitions.hpp" | ||
| #include "dca/phys/domains/cluster/symmetries/point_groups/no_symmetry.hpp" | ||
| #include "dca/phys/models/analytic_hamiltonians/util.hpp" | ||
|
|
||
| namespace dca { | ||
| namespace phys { | ||
| namespace models { | ||
| // dca::phys::models:: | ||
|
|
||
| template <typename point_group_type> | ||
| class complex_square_lattice { | ||
| public: | ||
| static constexpr bool complex_g0 = true; | ||
| static constexpr bool spin_symmetric = true; | ||
|
|
||
| typedef domains::no_symmetry<2> LDA_point_group; | ||
| typedef point_group_type DCA_point_group; | ||
|
|
||
| const static int DIMENSION = 2; | ||
| const static int BANDS = 1; | ||
|
|
||
| static const double* initializeRDCABasis(); | ||
| static const double* initializeRLDABasis(); | ||
|
|
||
| constexpr static int transformationSignOfR(int, int, int) { | ||
| return 1; | ||
| } | ||
| constexpr static int transformationSignOfK(int, int, int) { | ||
| return 1; | ||
| } | ||
|
|
||
| static std::vector<int> flavors(); | ||
| static std::vector<std::vector<double>> aVectors(); | ||
|
|
||
| static std::vector<std::pair<std::pair<int, int>, std::pair<int, int>>> orbitalPermutations(); | ||
|
|
||
| // Initializes the interaction part of the real space Hubbard Hamiltonian. | ||
| template <typename BandDmn, typename SpinDmn, typename RDmn, typename parameters_type> | ||
| static void initializeHInteraction( | ||
| func::function<typename parameters_type::Real, func::dmn_variadic<func::dmn_variadic<BandDmn, SpinDmn>, | ||
| func::dmn_variadic<BandDmn, SpinDmn>, RDmn>>& H_interaction, | ||
| const parameters_type& parameters); | ||
|
|
||
| template <class domain> | ||
| static void initializeHSymmetry(func::function<int, domain>& H_symmetry); | ||
|
|
||
| // Initializes the tight-binding (non-interacting) part of the momentum space Hamiltonian. | ||
| // Preconditions: The elements of KDmn are two-dimensional (access through index 0 and 1). | ||
| template <typename ParametersType, typename ScalarType, typename BandDmn, typename SpinDmn, typename KDmn> | ||
| static void initializeH0( | ||
| const ParametersType& parameters, | ||
| func::function<ScalarType, func::dmn_variadic<func::dmn_variadic<BandDmn, SpinDmn>, | ||
| func::dmn_variadic<BandDmn, SpinDmn>, KDmn>>& H_0); | ||
|
|
||
| template <typename ParametersType, typename ScalarType, typename BandDmn, typename SpinDmn, typename KDmn> | ||
| static void initializeH0WithQ( | ||
| const ParametersType& parameters, | ||
| func::function<ScalarType, func::dmn_variadic<func::dmn_variadic<BandDmn, SpinDmn>, | ||
| func::dmn_variadic<BandDmn, SpinDmn>, KDmn>>& H_0, typename KDmn::element_type& q); | ||
|
|
||
| }; | ||
|
|
||
| template <typename point_group_type> | ||
| const double* complex_square_lattice<point_group_type>::initializeRDCABasis() { | ||
| static double* r_DCA = new double[4]; | ||
|
|
||
| r_DCA[0] = 1.; | ||
| r_DCA[1] = 0.; | ||
| r_DCA[2] = 0.; | ||
| r_DCA[3] = 1.; | ||
|
|
||
| return r_DCA; | ||
| } | ||
|
|
||
| template <typename point_group_type> | ||
| const double* complex_square_lattice<point_group_type>::initializeRLDABasis() { | ||
| static double* r_LDA = new double[4]; | ||
|
|
||
| r_LDA[0] = 1.; | ||
| r_LDA[1] = 0.; | ||
| r_LDA[2] = 0.; | ||
| r_LDA[3] = 1.; | ||
|
|
||
| return r_LDA; | ||
| } | ||
|
|
||
| template <typename point_group_type> | ||
| std::vector<int> complex_square_lattice<point_group_type>::flavors() { | ||
| static std::vector<int> flavors(BANDS); | ||
|
|
||
| for (int i = 0; i < BANDS; i++) | ||
| flavors[i] = i; | ||
|
|
||
| return flavors; | ||
| } | ||
|
|
||
| template <typename point_group_type> | ||
| std::vector<std::vector<double>> complex_square_lattice<point_group_type>::aVectors() { | ||
| static std::vector<std::vector<double>> a_vecs(BANDS, std::vector<double>(DIMENSION, 0.)); | ||
| return a_vecs; | ||
| } | ||
|
|
||
| template <typename point_group_type> | ||
| std::vector<std::pair<std::pair<int, int>, std::pair<int, int>>> complex_square_lattice< | ||
| point_group_type>::orbitalPermutations() { | ||
| static std::vector<std::pair<std::pair<int, int>, std::pair<int, int>>> permutations(0); | ||
| return permutations; | ||
| } | ||
|
|
||
| template <typename point_group_type> | ||
| template <typename BandDmn, typename SpinDmn, typename RDmn, typename parameters_type> | ||
| void complex_square_lattice<point_group_type>::initializeHInteraction( | ||
| func::function<typename parameters_type::Real, func::dmn_variadic<func::dmn_variadic<BandDmn, SpinDmn>, | ||
| func::dmn_variadic<BandDmn, SpinDmn>, RDmn>>& H_interaction, | ||
| const parameters_type& parameters) { | ||
| if (BandDmn::dmn_size() != BANDS) | ||
| throw std::logic_error("Square lattice has one band."); | ||
| if (SpinDmn::dmn_size() != 2) | ||
| throw std::logic_error("Spin domain size must be 2."); | ||
|
|
||
| const std::vector<typename RDmn::parameter_type::element_type>& basis = | ||
| RDmn::parameter_type::get_basis_vectors(); | ||
|
|
||
| assert(basis.size() == 2); | ||
|
|
||
| // There are two different nearest neighbor (nn) pairs: along the basis vector a1 and along the | ||
| // basis vector a2. | ||
| const std::vector<typename RDmn::parameter_type::element_type>& nn_vec(basis); | ||
|
|
||
| // Compute indices of nearest neighbors (nn) w.r.t. origin. | ||
| std::vector<int> nn_index; | ||
|
|
||
| const std::vector<typename RDmn::parameter_type::element_type>& super_basis = | ||
| RDmn::parameter_type::get_super_basis_vectors(); | ||
| const std::vector<typename RDmn::parameter_type::element_type>& elements = | ||
| RDmn::parameter_type::get_elements(); | ||
|
|
||
| for (const auto& vec : nn_vec) { | ||
| std::vector<double> nn_vec_translated = | ||
| domains::cluster_operations::translate_inside_cluster(vec, super_basis); | ||
| nn_index.push_back( | ||
| domains::cluster_operations::index(nn_vec_translated, elements, domains::BRILLOUIN_ZONE)); | ||
| } | ||
|
|
||
| H_interaction = 0; | ||
|
|
||
| const double V = parameters.get_V(); | ||
| for (auto index : nn_index) { | ||
| H_interaction(0, 0, 0, 1, index) = V; | ||
| H_interaction(0, 1, 0, 0, index) = V; | ||
| } | ||
|
|
||
| // Nearest-neighbor same spin interaction | ||
| const double V_prime = parameters.get_V_prime(); | ||
| for (auto index : nn_index) { | ||
| H_interaction(0, 0, 0, 0, index) = V_prime; | ||
| H_interaction(0, 1, 0, 1, index) = V_prime; | ||
| } | ||
|
|
||
| // Get the index of the origin (0,0). | ||
| const int origin = RDmn::parameter_type::origin_index(); | ||
|
|
||
| // On-site interaction | ||
| // This has to be set last since for small clusters a nearest neighbor might | ||
| // be the same site and therefore V would overwrite U. | ||
| const double U = parameters.get_U(); | ||
| H_interaction(0, 0, 0, 1, origin) = U; | ||
| H_interaction(0, 1, 0, 0, origin) = U; | ||
|
|
||
| // util::initializeSingleBandHint(parameters, nn_vec, H_interactioneraction); | ||
| } | ||
|
|
||
| template <typename point_group_type> | ||
| template <class domain> | ||
| void complex_square_lattice<point_group_type>::initializeHSymmetry(func::function<int, domain>& H_symmetries) { | ||
| H_symmetries(0, 0) = 0; | ||
| H_symmetries(0, 1) = -1; | ||
| H_symmetries(1, 0) = -1; | ||
| H_symmetries(1, 1) = 0; | ||
| } | ||
|
|
||
| template <typename point_group_type> | ||
| template <typename ParametersType, typename ScalarType, typename BandDmn, typename SpinDmn, typename KDmn> | ||
| void complex_square_lattice<point_group_type>::initializeH0( | ||
| const ParametersType& parameters, | ||
| func::function<ScalarType, func::dmn_variadic<func::dmn_variadic<BandDmn, SpinDmn>, | ||
| func::dmn_variadic<BandDmn, SpinDmn>, KDmn>>& H_0) { | ||
| typename KDmn::element_type default_q; | ||
| initializeH0WithQ(parameters, H_0, default_q); | ||
| } | ||
|
|
||
| template <typename point_group_type> | ||
| template <typename ParametersType, typename ScalarType, typename BandDmn, typename SpinDmn, typename KDmn> | ||
| void complex_square_lattice<point_group_type>::initializeH0WithQ( | ||
| const ParametersType& parameters, | ||
| func::function<ScalarType, func::dmn_variadic<func::dmn_variadic<BandDmn, SpinDmn>, | ||
| func::dmn_variadic<BandDmn, SpinDmn>, KDmn>>& H_0, typename KDmn::element_type& q [[maybe_unused]]) { | ||
| if (BandDmn::dmn_size() != BANDS) | ||
| throw std::logic_error("Square lattice has one band."); | ||
| if (SpinDmn::dmn_size() != 2) | ||
| throw std::logic_error("Spin domain size must be 2."); | ||
|
|
||
| const auto& k_vecs = KDmn::get_elements(); | ||
|
|
||
| const auto t = parameters.get_t(); | ||
| const auto t_prime = parameters.get_t_prime(); | ||
|
|
||
| H_0 = ScalarType(0); | ||
|
|
||
| for (int k_ind = 0; k_ind < KDmn::dmn_size(); ++k_ind) { | ||
| const auto& k = k_vecs[k_ind]; | ||
| const auto val = | ||
| -2. * t * (std::cos(k[0]) + std::cos(k[1])) - 4. * t_prime * std::cos(k[0]) * std::cos(k[1]); | ||
|
|
||
| H_0(0, 0, 0, 0, k_ind) = val; | ||
| H_0(0, 1, 0, 1, k_ind) = val; | ||
| } | ||
| } | ||
|
|
||
| } // namespace models | ||
| } // namespace phys | ||
| } // namespace dca | ||
|
|
||
| #endif // DCA_PHYS_MODELS_ANALYTIC_HAMILTONIANS_COMPLEX_SQUARE_LATTICE_HPP |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters