From 5f4547127899cd7ec6177f191a780d1626c4b53d Mon Sep 17 00:00:00 2001 From: guanjihuan Date: Fri, 12 Aug 2022 13:57:03 +0800 Subject: [PATCH] Create calculation_of_Chern_number_by_Wilson_loop_for_degenerate_case.py --- ...mber_by_Wilson_loop_for_degenerate_case.py | 109 ++++++++++++++++++ 1 file changed, 109 insertions(+) create mode 100644 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 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 new file mode 100644 index 0000000..79dc1a6 --- /dev/null +++ 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 @@ -0,0 +1,109 @@ +""" +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/23989 +""" + +import numpy as np +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_Wilson_loop_for_degenerate_case(H_k, num_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, num_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, num_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, num_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, num_of_bands=[0, 1], precision_of_plaquettes=20, precision_of_Wilson_loop=5, print_show=0): + import math + delta = 2*math.pi/precision_of_plaquettes + 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): + vector_array = [] + # line_1 + 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) + 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) + 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) + eigenvalue, eigenvector = np.linalg.eig(H_delta) + vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))] + vector_array.append(vector_delta) + Wilson_loop = 1 + dim = len(num_of_bands) + for i0 in range(len(vector_array)-1): + dot_matrix = np.zeros((dim , dim), dtype=complex) + i01 = 0 + for dim1 in num_of_bands: + i02 = 0 + for dim2 in num_of_bands: + dot_matrix[i01, i02] = np.dot(vector_array[i0][:, dim1].transpose().conj(), vector_array[i0+1][:, dim2]) + i02 += 1 + i01 += 1 + det_value = np.linalg.det(dot_matrix) + Wilson_loop = Wilson_loop*det_value + dot_matrix_plus = np.zeros((dim , dim), dtype=complex) + i01 = 0 + for dim1 in num_of_bands: + i02 = 0 + for dim2 in num_of_bands: + dot_matrix_plus[i01, i02] = np.dot(vector_array[len(vector_array)-1][:, dim1].transpose().conj(), vector_array[0][:, dim2]) + i02 += 1 + i01 += 1 + det_value = np.linalg.det(dot_matrix_plus) + 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 + + +if __name__ == '__main__': + main() \ No newline at end of file