update

academic_codes/2021.12.28_calculation_of_Chern_number_by_Wilson_loop/calculation_of_Chern_number_by_Wilson_loop.py

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+"""
+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
+"""
+
+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)
+
+            angle = np.log(np.dot(np.dot(np.dot(line_1, line_2), line_3), line_4))/1j
+            chern_number = chern_number + angle
+    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()