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Update calculation_of_Chern_number_by_Wilson_loop_for_degenerate_case.py

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guanjihuan 2022-08-13 07:01:25 +08:00
parent 625ae9918b
commit 6c833ecec6
1 changed files with 18 additions and 18 deletions
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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
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@ -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 numpy as np
import math
from math import * from math import *
import cmath import cmath
import functools import functools
@ -27,24 +28,23 @@ def main():
Ny = 20 Ny = 20
H_k = functools.partial(hamiltonian, Ny=Ny, B=1/Ny) 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('价带：', chern_number)
print() 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('价带（包含两个交叉能带）：', chern_number)
print() 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) 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 # # 函数可通过Guan软件包调用。安装方法：pip install --upgrade guan
# import 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): 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
delta = 2*math.pi/precision_of_plaquettes delta = 2*math.pi/precision_of_plaquettes
chern_number = 0 chern_number = 0
for kx in np.arange(-math.pi, math.pi, delta): 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): for ky in np.arange(-math.pi, math.pi, delta):
vector_array = [] vector_array = []
# line_1 # line_1
for i0 in range(precision_of_Wilson_loop): for i0 in range(precision_of_wilson_loop):
H_delta = hamiltonian_function(kx+delta/precision_of_Wilson_loop*i0, ky) H_delta = hamiltonian_function(kx+delta/precision_of_wilson_loop*i0, ky)
eigenvalue, eigenvector = np.linalg.eig(H_delta) eigenvalue, eigenvector = np.linalg.eig(H_delta)
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))] vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
vector_array.append(vector_delta) vector_array.append(vector_delta)
# line_2 # line_2
for i0 in range(precision_of_Wilson_loop): for i0 in range(precision_of_wilson_loop):
H_delta = hamiltonian_function(kx+delta, ky+delta/precision_of_Wilson_loop*i0) H_delta = hamiltonian_function(kx+delta, ky+delta/precision_of_wilson_loop*i0)
eigenvalue, eigenvector = np.linalg.eig(H_delta) eigenvalue, eigenvector = np.linalg.eig(H_delta)
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))] vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
vector_array.append(vector_delta) vector_array.append(vector_delta)
# line_3 # line_3
for i0 in range(precision_of_Wilson_loop): for i0 in range(precision_of_wilson_loop):
H_delta = hamiltonian_function(kx+delta-delta/precision_of_Wilson_loop*i0, ky+delta) H_delta = hamiltonian_function(kx+delta-delta/precision_of_wilson_loop*i0, ky+delta)
eigenvalue, eigenvector = np.linalg.eig(H_delta) eigenvalue, eigenvector = np.linalg.eig(H_delta)
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))] vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
vector_array.append(vector_delta) vector_array.append(vector_delta)
# line_4 # line_4
for i0 in range(precision_of_Wilson_loop): for i0 in range(precision_of_wilson_loop):
H_delta = hamiltonian_function(kx, ky+delta-delta/precision_of_Wilson_loop*i0) H_delta = hamiltonian_function(kx, ky+delta-delta/precision_of_wilson_loop*i0)
eigenvalue, eigenvector = np.linalg.eig(H_delta) eigenvalue, eigenvector = np.linalg.eig(H_delta)
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))] vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))]
vector_array.append(vector_delta) vector_array.append(vector_delta)
Wilson_loop = 1 wilson_loop = 1
dim = len(index_of_bands) dim = len(index_of_bands)
for i0 in range(len(vector_array)-1): for i0 in range(len(vector_array)-1):
dot_matrix = np.zeros((dim , dim), dtype=complex) 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 i02 += 1
i01 += 1 i01 += 1
det_value = np.linalg.det(dot_matrix) 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) dot_matrix_plus = np.zeros((dim , dim), dtype=complex)
i01 = 0 i01 = 0
for dim1 in index_of_bands: 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 i02 += 1
i01 += 1 i01 += 1
det_value = np.linalg.det(dot_matrix_plus) det_value = np.linalg.det(dot_matrix_plus)
Wilson_loop = Wilson_loop*det_value wilson_loop = wilson_loop*det_value
arg = np.log(Wilson_loop)/1j arg = np.log(wilson_loop)/1j
chern_number = chern_number + arg chern_number = chern_number + arg
chern_number = chern_number/(2*math.pi) chern_number = chern_number/(2*math.pi)
return chern_number return chern_number