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 59d6c44..316df87 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 @@ -4,6 +4,7 @@ The newest version of this code is on the web page: https://www.guanjihuan.com/a """ import numpy as np +import math from math import * import cmath import functools @@ -27,24 +28,23 @@ 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) + 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() - chern_number = calculate_chern_number_for_square_lattice_with_Wilson_loop_for_degenerate_case(H_k, index_of_bands=range(int(Ny/2)+2), precision_of_Wilson_loop=5) + chern_number = calculate_chern_number_for_square_lattice_with_wilson_loop_for_degenerate_case(H_k, index_of_bands=range(int(Ny/2)+2), precision_of_wilson_loop=5) print('价带（包含两个交叉能带）：', chern_number) print() - chern_number = calculate_chern_number_for_square_lattice_with_Wilson_loop_for_degenerate_case(H_k, index_of_bands=range(Ny), precision_of_Wilson_loop=5) + chern_number = calculate_chern_number_for_square_lattice_with_wilson_loop_for_degenerate_case(H_k, index_of_bands=range(Ny), precision_of_wilson_loop=5) 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_Wilson_loop_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], precision_of_plaquettes=20, precision_of_Wilson_loop=5, print_show=0) + # chern_number = guan.calculate_chern_number_for_square_lattice_with_wilson_loop_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], precision_of_plaquettes=20, precision_of_wilson_loop=5, print_show=0) -def calculate_chern_number_for_square_lattice_with_Wilson_loop_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], precision_of_plaquettes=20, precision_of_Wilson_loop=5, print_show=0): - import math +def calculate_chern_number_for_square_lattice_with_wilson_loop_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], precision_of_plaquettes=20, precision_of_wilson_loop=5, print_show=0): delta = 2*math.pi/precision_of_plaquettes chern_number = 0 for kx in np.arange(-math.pi, math.pi, delta): @@ -53,30 +53,30 @@ def calculate_chern_number_for_square_lattice_with_Wilson_loop_for_degenerate_ca for ky in np.arange(-math.pi, math.pi, delta): vector_array = [] # line_1 - for i0 in range(precision_of_Wilson_loop): - H_delta = hamiltonian_function(kx+delta/precision_of_Wilson_loop*i0, ky) + for i0 in range(precision_of_wilson_loop): + H_delta = hamiltonian_function(kx+delta/precision_of_wilson_loop*i0, ky) eigenvalue, eigenvector = np.linalg.eig(H_delta) vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))] vector_array.append(vector_delta) # line_2 - for i0 in range(precision_of_Wilson_loop): - H_delta = hamiltonian_function(kx+delta, ky+delta/precision_of_Wilson_loop*i0) + for i0 in range(precision_of_wilson_loop): + H_delta = hamiltonian_function(kx+delta, ky+delta/precision_of_wilson_loop*i0) eigenvalue, eigenvector = np.linalg.eig(H_delta) vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))] vector_array.append(vector_delta) # line_3 - for i0 in range(precision_of_Wilson_loop): - H_delta = hamiltonian_function(kx+delta-delta/precision_of_Wilson_loop*i0, ky+delta) + for i0 in range(precision_of_wilson_loop): + H_delta = hamiltonian_function(kx+delta-delta/precision_of_wilson_loop*i0, ky+delta) eigenvalue, eigenvector = np.linalg.eig(H_delta) vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))] vector_array.append(vector_delta) # line_4 - for i0 in range(precision_of_Wilson_loop): - H_delta = hamiltonian_function(kx, ky+delta-delta/precision_of_Wilson_loop*i0) + for i0 in range(precision_of_wilson_loop): + H_delta = hamiltonian_function(kx, ky+delta-delta/precision_of_wilson_loop*i0) eigenvalue, eigenvector = np.linalg.eig(H_delta) vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))] vector_array.append(vector_delta) - Wilson_loop = 1 + wilson_loop = 1 dim = len(index_of_bands) for i0 in range(len(vector_array)-1): dot_matrix = np.zeros((dim , dim), dtype=complex) @@ -88,7 +88,7 @@ def calculate_chern_number_for_square_lattice_with_Wilson_loop_for_degenerate_ca i02 += 1 i01 += 1 det_value = np.linalg.det(dot_matrix) - Wilson_loop = Wilson_loop*det_value + wilson_loop = wilson_loop*det_value dot_matrix_plus = np.zeros((dim , dim), dtype=complex) i01 = 0 for dim1 in index_of_bands: @@ -98,8 +98,8 @@ def calculate_chern_number_for_square_lattice_with_Wilson_loop_for_degenerate_ca i02 += 1 i01 += 1 det_value = np.linalg.det(dot_matrix_plus) - Wilson_loop = Wilson_loop*det_value - arg = np.log(Wilson_loop)/1j + wilson_loop = wilson_loop*det_value + arg = np.log(wilson_loop)/1j chern_number = chern_number + arg chern_number = chern_number/(2*math.pi) return chern_number