From eaaff6b7f97a7f3284101e7127a904390a673510 Mon Sep 17 00:00:00 2001 From: guanjihuan Date: Sun, 28 Aug 2022 01:54:15 +0800 Subject: [PATCH] update --- ...mber_by_Wilson_loop_for_degenerate_case.py | 1 + ...bution_with_Wilson_loop_(function_form).py | 0 ...oop_for_degenerate_case_(function_form).py | 0 ...th_the_efficient_method_(function_form).py | 0 ...by_efficient_method_for_degenerate_case.py | 116 ++++++++++++++++++ 5 files changed, 117 insertions(+) rename academic_codes/{2022_08_13_Berry_curvature_distribution_in_function_form => 2022.08.13_Berry_curvature_distribution_in_function_form}/Berry_curvature_distribution_with_Wilson_loop_(function_form).py (100%) rename academic_codes/{2022_08_13_Berry_curvature_distribution_in_function_form => 2022.08.13_Berry_curvature_distribution_in_function_form}/Berry_curvature_distribution_with_Wilson_loop_for_degenerate_case_(function_form).py (100%) rename academic_codes/{2022_08_13_Berry_curvature_distribution_in_function_form => 2022.08.13_Berry_curvature_distribution_in_function_form}/Berry_curvature_distribution_with_the_efficient_method_(function_form).py (100%) create mode 100644 academic_codes/2022.08.28_calculation_of_Chern_number_by_efficient_method_for_degenerate_case/calculation_of_Chern_number_by_efficient_method_for_degenerate_case.py diff --git a/academic_codes/2022.08.12_calculation_of_Chern_number_by_Wilson_loop_for_degenerate_case/calculation_of_Chern_number_by_Wilson_loop_for_degenerate_case.py b/academic_codes/2022.08.12_calculation_of_Chern_number_by_Wilson_loop_for_degenerate_case/calculation_of_Chern_number_by_Wilson_loop_for_degenerate_case.py index 316df87..9e8e9e3 100644 --- a/academic_codes/2022.08.12_calculation_of_Chern_number_by_Wilson_loop_for_degenerate_case/calculation_of_Chern_number_by_Wilson_loop_for_degenerate_case.py +++ b/academic_codes/2022.08.12_calculation_of_Chern_number_by_Wilson_loop_for_degenerate_case/calculation_of_Chern_number_by_Wilson_loop_for_degenerate_case.py @@ -28,6 +28,7 @@ def main(): Ny = 20 H_k = functools.partial(hamiltonian, Ny=Ny, B=1/Ny) + chern_number = calculate_chern_number_for_square_lattice_with_wilson_loop_for_degenerate_case(H_k, index_of_bands=range(int(Ny/2)-1), precision_of_wilson_loop=5) print('价带：', chern_number) print() diff --git a/academic_codes/2022_08_13_Berry_curvature_distribution_in_function_form/Berry_curvature_distribution_with_Wilson_loop_(function_form).py b/academic_codes/2022.08.13_Berry_curvature_distribution_in_function_form/Berry_curvature_distribution_with_Wilson_loop_(function_form).py similarity index 100% rename from academic_codes/2022_08_13_Berry_curvature_distribution_in_function_form/Berry_curvature_distribution_with_Wilson_loop_(function_form).py rename to academic_codes/2022.08.13_Berry_curvature_distribution_in_function_form/Berry_curvature_distribution_with_Wilson_loop_(function_form).py diff --git a/academic_codes/2022_08_13_Berry_curvature_distribution_in_function_form/Berry_curvature_distribution_with_Wilson_loop_for_degenerate_case_(function_form).py b/academic_codes/2022.08.13_Berry_curvature_distribution_in_function_form/Berry_curvature_distribution_with_Wilson_loop_for_degenerate_case_(function_form).py similarity index 100% rename from academic_codes/2022_08_13_Berry_curvature_distribution_in_function_form/Berry_curvature_distribution_with_Wilson_loop_for_degenerate_case_(function_form).py rename to academic_codes/2022.08.13_Berry_curvature_distribution_in_function_form/Berry_curvature_distribution_with_Wilson_loop_for_degenerate_case_(function_form).py diff --git a/academic_codes/2022_08_13_Berry_curvature_distribution_in_function_form/Berry_curvature_distribution_with_the_efficient_method_(function_form).py b/academic_codes/2022.08.13_Berry_curvature_distribution_in_function_form/Berry_curvature_distribution_with_the_efficient_method_(function_form).py similarity index 100% rename from academic_codes/2022_08_13_Berry_curvature_distribution_in_function_form/Berry_curvature_distribution_with_the_efficient_method_(function_form).py rename to academic_codes/2022.08.13_Berry_curvature_distribution_in_function_form/Berry_curvature_distribution_with_the_efficient_method_(function_form).py diff --git a/academic_codes/2022.08.28_calculation_of_Chern_number_by_efficient_method_for_degenerate_case/calculation_of_Chern_number_by_efficient_method_for_degenerate_case.py b/academic_codes/2022.08.28_calculation_of_Chern_number_by_efficient_method_for_degenerate_case/calculation_of_Chern_number_by_efficient_method_for_degenerate_case.py new file mode 100644 index 0000000..0ae3dd7 --- /dev/null +++ b/academic_codes/2022.08.28_calculation_of_Chern_number_by_efficient_method_for_degenerate_case/calculation_of_Chern_number_by_efficient_method_for_degenerate_case.py @@ -0,0 +1,116 @@ +""" +This code is supported by the website: https://www.guanjihuan.com +The newest version of this code is on the web page: https://www.guanjihuan.com/archives/25107 +""" + +import numpy as np +import math +from math import * +import cmath +import functools + + +def hamiltonian(kx, ky, Ny, B): + h00 = np.zeros((Ny, Ny), dtype=complex) + h01 = np.zeros((Ny, Ny), dtype=complex) + t = 1 + for iy in range(Ny-1): + h00[iy, iy+1] = t + h00[iy+1, iy] = t + h00[Ny-1, 0] = t*cmath.exp(1j*ky) + h00[0, Ny-1] = t*cmath.exp(-1j*ky) + for iy in range(Ny): + h01[iy, iy] = t*cmath.exp(-2*np.pi*1j*B*iy) + matrix = h00 + h01*cmath.exp(1j*kx) + h01.transpose().conj()*cmath.exp(-1j*kx) + return matrix + + +def main(): + Ny = 20 + + H_k = functools.partial(hamiltonian, Ny=Ny, B=1/Ny) + + chern_number = calculate_chern_number_for_square_lattice_with_efficient_method_for_degenerate_case(H_k, index_of_bands=range(int(Ny/2)-1)) + print('价带：', chern_number) + print() + + chern_number = calculate_chern_number_for_square_lattice_with_efficient_method_for_degenerate_case(H_k, index_of_bands=range(int(Ny/2)+2)) + print('价带（包含两个交叉能带）：', chern_number) + print() + + chern_number = calculate_chern_number_for_square_lattice_with_efficient_method_for_degenerate_case(H_k, index_of_bands=range(Ny)) + print('所有能带：', chern_number) + + # 函数可通过Guan软件包调用。安装方法：pip install --upgrade guan + # import guan + # chern_number = guan.calculate_chern_number_for_square_lattice_with_efficient_method_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], precision=100, print_show=0) + + +def calculate_chern_number_for_square_lattice_with_efficient_method_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], precision=100, print_show=0): + delta = 2*math.pi/precision + chern_number = 0 + for kx in np.arange(-math.pi, math.pi, delta): + if print_show == 1: + print(kx) + for ky in np.arange(-math.pi, math.pi, delta): + H = hamiltonian_function(kx, ky) + eigenvalue, vector = np.linalg.eigh(H) + H_delta_kx = hamiltonian_function(kx+delta, ky) + eigenvalue, vector_delta_kx = np.linalg.eigh(H_delta_kx) + H_delta_ky = hamiltonian_function(kx, ky+delta) + eigenvalue, vector_delta_ky = np.linalg.eigh(H_delta_ky) + H_delta_kx_ky = hamiltonian_function(kx+delta, ky+delta) + eigenvalue, vector_delta_kx_ky = np.linalg.eigh(H_delta_kx_ky) + dim = len(index_of_bands) + det_value = 1 + # first dot + dot_matrix = np.zeros((dim , dim), dtype=complex) + i0 = 0 + for dim1 in index_of_bands: + j0 = 0 + for dim2 in index_of_bands: + dot_matrix[dim1, dim2] = np.dot(np.conj(vector[:, dim1]), vector_delta_kx[:, dim2]) + j0 += 1 + i0 += 1 + dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix)) + det_value = det_value*dot_matrix + # second dot + dot_matrix = np.zeros((dim , dim), dtype=complex) + i0 = 0 + for dim1 in index_of_bands: + j0 = 0 + for dim2 in index_of_bands: + dot_matrix[dim1, dim2] = np.dot(np.conj(vector_delta_kx[:, dim1]), vector_delta_kx_ky[:, dim2]) + j0 += 1 + i0 += 1 + dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix)) + det_value = det_value*dot_matrix + # third dot + dot_matrix = np.zeros((dim , dim), dtype=complex) + i0 = 0 + for dim1 in index_of_bands: + j0 = 0 + for dim2 in index_of_bands: + dot_matrix[dim1, dim2] = np.dot(np.conj(vector_delta_kx_ky[:, dim1]), vector_delta_ky[:, dim2]) + j0 += 1 + i0 += 1 + dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix)) + det_value = det_value*dot_matrix + # four dot + dot_matrix = np.zeros((dim , dim), dtype=complex) + i0 = 0 + for dim1 in index_of_bands: + j0 = 0 + for dim2 in index_of_bands: + dot_matrix[dim1, dim2] = np.dot(np.conj(vector_delta_ky[:, dim1]), vector[:, dim2]) + j0 += 1 + i0 += 1 + dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix)) + det_value= det_value*dot_matrix + chern_number += cmath.log(det_value) + chern_number = chern_number/(2*math.pi*1j) + return chern_number + + +if __name__ == '__main__': + main() \ No newline at end of file