update

2021.07.26_calculation_of_chern_number_with_kubo_formula/calculation_of_chern_number_with_kubo_formula.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/16148
+"""
+
+import numpy as np
+from math import *
+import time
+
+
+def hamiltonian(kx, ky):  # one QAH model with Chern number = 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       # integration
+    delta = 1e-6  # derivation
+    chern_number = 0 
+    for kx in np.arange(-pi, pi, 2*pi/n):
+        for ky in np.arange(-pi, pi,2*pi/n):
+            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()