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guanjihuan 2022-01-04 16:32:08 +08:00
parent 7b92011a54
commit 083669875f
2 changed files with 102 additions and 26 deletions
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61
academic_codes/2021.12.28_calculation_of_Chern_number_by_Wilson_loop/calculation_of_Chern_number_by_Wilson_loop.py
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@ -24,39 +24,48 @@ def hamiltonian(kx, ky): # 量子反常霍尔QAH模型（该参数对应的陈
def main():
start_time = time.time()
n = 100 # 积分密度
delta = 2*pi/n
n1 = 10 # small plaquettes精度
n2 = 800 # Wilson loop精度
delta = 2*pi/n1
chern_number = 0
for kx in np.arange(-pi, pi, delta):
for ky in np.arange(-pi, pi, delta):
H = hamiltonian(kx, ky)
eigenvalue, eigenvector = np.linalg.eig(H)
vector = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] # 价带波函数
# vector = eigenvector[:, np.argsort(np.real(eigenvalue))[0]]*cmath.exp(1j*np.random.uniform(0, pi)) # 验证规范不依赖性
H_delta_kx = hamiltonian(kx+delta, ky)
eigenvalue, eigenvector = np.linalg.eig(H_delta_kx)
vector_delta_kx = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] # 略偏离kx的波函数
H_delta_ky = hamiltonian(kx, ky+delta)
eigenvalue, eigenvector = np.linalg.eig(H_delta_ky)
vector_delta_ky = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] # 略偏离ky的波函数
H_delta_kx_ky = hamiltonian(kx+delta, ky+delta)
eigenvalue, eigenvector = np.linalg.eig(H_delta_kx_ky)
vector_delta_kx_ky = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] # 略偏离kx和ky的波函数
line_1 = np.dot(vector.transpose().conj(), vector_delta_kx)
line_2 = np.dot(vector_delta_kx.transpose().conj(), vector_delta_kx_ky)
line_3 = np.dot(vector_delta_kx_ky.transpose().conj(), vector_delta_ky)
line_4 = np.dot(vector_delta_ky.transpose().conj(), vector)
arg = np.log(np.dot(np.dot(np.dot(line_1, line_2), line_3), line_4))/1j
vector_array = []
# line_1
for i2 in range(n2+1):
H_delta = hamiltonian(kx+delta/n2*i2, ky)
eigenvalue, eigenvector = np.linalg.eig(H_delta)
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))[0]]
# vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))[0]]*cmath.exp(1j*np.random.uniform(0, pi)) # 验证规范不依赖性
vector_array.append(vector_delta)
# line_2
for i2 in range(n2):
H_delta = hamiltonian(kx+delta, ky+delta/n2*(i2+1))
eigenvalue, eigenvector = np.linalg.eig(H_delta)
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))[0]]
vector_array.append(vector_delta)
# line_3
for i2 in range(n2):
H_delta = hamiltonian(kx+delta-delta/n2*(i2+1), ky+delta)
eigenvalue, eigenvector = np.linalg.eig(H_delta)
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))[0]]
vector_array.append(vector_delta)
# line_4
for i2 in range(n2-1):
H_delta = hamiltonian(kx, ky+delta-delta/n2*(i2+1))
eigenvalue, eigenvector = np.linalg.eig(H_delta)
vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))[0]]
vector_array.append(vector_delta)
Wilson_loop = 1
for i0 in range(len(vector_array)-1):
Wilson_loop = Wilson_loop*np.dot(vector_array[i0].transpose().conj(), vector_array[i0+1])
Wilson_loop = Wilson_loop*np.dot(vector_array[len(vector_array)-1].transpose().conj(), vector_array[0])
arg = np.log(Wilson_loop)/1j
chern_number = chern_number + arg
chern_number = chern_number/(2*pi)
print('Chern number = ', chern_number)
end_time = time.time()
print('运行时间(min)=', (end_time-start_time)/60)
print('运行时间（秒）=', end_time-start_time)
if __name__ == '__main__':

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academic_codes/2021.12.28_calculation_of_Chern_number_by_Wilson_loop/calculation_of_Chern_number_by_Wilson_loop_(wrong).py Normal file
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@ -0,0 +1,67 @@
"""
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/18319
"""
"""
Notice that this code is not correct for calculating the Chern number because of the low precision in the calculation of Wilson loop!
"""
import numpy as np
from math import *
import time
import cmath
def hamiltonian(kx, ky): # 量子反常霍尔QAH模型（该参数对应的陈数为2）
t1 = 1.0
t2 = 1.0
t3 = 0.5
m = -1.0
matrix = np.zeros((2, 2), dtype=complex)
matrix[0, 1] = 2*t1*cos(kx)-1j*2*t1*cos(ky)
matrix[1, 0] = 2*t1*cos(kx)+1j*2*t1*cos(ky)
matrix[0, 0] = m+2*t3*sin(kx)+2*t3*sin(ky)+2*t2*cos(kx+ky)
matrix[1, 1] = -(m+2*t3*sin(kx)+2*t3*sin(ky)+2*t2*cos(kx+ky))
return matrix
def main():
start_time = time.time()
n = 200 # 积分密度
delta = 2*pi/n
chern_number = 0
for kx in np.arange(-pi, pi, delta):
for ky in np.arange(-pi, pi, delta):
H = hamiltonian(kx, ky)
eigenvalue, eigenvector = np.linalg.eig(H)
vector = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] # 价带波函数
# vector = eigenvector[:, np.argsort(np.real(eigenvalue))[0]]*cmath.exp(1j*np.random.uniform(0, pi)) # 验证规范不依赖性
H_delta_kx = hamiltonian(kx+delta, ky)
eigenvalue, eigenvector = np.linalg.eig(H_delta_kx)
vector_delta_kx = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] # 略偏离kx的波函数
H_delta_ky = hamiltonian(kx, ky+delta)
eigenvalue, eigenvector = np.linalg.eig(H_delta_ky)
vector_delta_ky = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] # 略偏离ky的波函数
H_delta_kx_ky = hamiltonian(kx+delta, ky+delta)
eigenvalue, eigenvector = np.linalg.eig(H_delta_kx_ky)
vector_delta_kx_ky = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] # 略偏离kx和ky的波函数
line_1 = np.dot(vector.transpose().conj(), vector_delta_kx)
line_2 = np.dot(vector_delta_kx.transpose().conj(), vector_delta_kx_ky)
line_3 = np.dot(vector_delta_kx_ky.transpose().conj(), vector_delta_ky)
line_4 = np.dot(vector_delta_ky.transpose().conj(), vector)
arg = np.log(np.dot(np.dot(np.dot(line_1, line_2), line_3), line_4))/1j
chern_number = chern_number + arg
chern_number = chern_number/(2*pi)
print('Chern number = ', chern_number)
end_time = time.time()
print('运行时间（秒）=', end_time-start_time)
if __name__ == '__main__':
main()