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guanjihuan 2021-07-26 03:34:21 +08:00
parent baf15fc0e4
commit 3a8dbc00c9
3 changed files with 55 additions and 7 deletions
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5
academic_codes/2020.01.05_calculation_of_Chern_number_by_definition_method/calculation_of_Chern_number_by_definition_method.py
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@ -4,8 +4,7 @@ The newest version of this code is on the web page: https://www.guanjihuan.com/a
"""
import numpy as np
import matplotlib.pyplot as plt
from math import * # 引入pi, cos等
from math import *
import time
@ -14,7 +13,7 @@ def hamiltonian(kx, ky): # 量子反常霍尔QAH模型（该参数对应的陈
t2 = 1.0
t3 = 0.5
m = -1.0
matrix = np.zeros((2, 2))*(1+0j)
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)

7
academic_codes/2020.01.05_calculation_of_Chern_number_by_definition_method/find_smooth_gauge_and_calculate_Chern_number.py
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@ -4,8 +4,7 @@ The newest version of this code is on the web page: https://www.guanjihuan.com/a
"""
import numpy as np
import matplotlib.pyplot as plt
from math import * # 引入pi, cos等
from math import *
import time
import cmath
@ -15,7 +14,7 @@ def hamiltonian(kx, ky): # 量子反常霍尔QAH模型（该参数对应的陈
t2 = 1.0
t3 = 0.5
m = -1.0
matrix = np.zeros((2, 2))*(1+0j)
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)
@ -76,7 +75,7 @@ def find_vector_with_the_same_gauge(vector_1, vector_0):
for i0 in range(n_test):
test_1 = np.sum(np.abs(vector_1*cmath.exp(1j*phase_1_pre) - vector_0))
test_2 = np.sum(np.abs(vector_1*cmath.exp(1j*phase_2_pre) - vector_0))
if test_1 < 1e-6:
if test_1 < 1e-8:
phase = phase_1_pre
# print('Done with i0=', i0)
break

50
academic_codes/2021.07.26_calculation_of_Berry_curvature_and_Chern_number_by_another_method/calculation_of_Berry_curvature_and_Chern_number_by_another_method.py Normal file
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@ -0,0 +1,50 @@
"""
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/16148
"""
import numpy as np
from math import *
import time
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
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_0 = eigenvector[:, np.argsort(np.real(eigenvalue))[0]]
vector_1 = eigenvector[:, np.argsort(np.real(eigenvalue))[1]]
eigenvalue = np.sort(np.real(eigenvalue))
H_delta_kx = hamiltonian(kx+delta, ky)-hamiltonian(kx, ky)
H_delta_ky = hamiltonian(kx, ky+delta)-hamiltonian(kx, ky)
berry_curvature = 1j*(np.dot(np.dot(np.dot(np.dot(np.dot(vector_0.transpose().conj(), H_delta_kx/delta), vector_1), vector_1.transpose().conj()), H_delta_ky/delta), vector_0)- np.dot(np.dot(np.dot(np.dot(np.dot(vector_0.transpose().conj(), H_delta_ky/delta), vector_1), vector_1.transpose().conj()), H_delta_kx/delta), vector_0))/(eigenvalue[0]-eigenvalue[1])**2
chern_number = chern_number + berry_curvature*(2*pi/n)**2
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)
if __name__ == '__main__':
main()