update

2020.07.26_Hamiltonian_bands_and_Winding_number_in_SSH_model/Winding_number_in_SSH_model.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/5025
+"""
+
+
+import numpy as np
+import matplotlib.pyplot as plt
+from math import * 
+import cmath
+import time
+
+def hamiltonian(k):  # SSH模型
+    v=0.6
+    w=1
+    matrix = np.zeros((2, 2), dtype=complex)
+    matrix[0,1] = v+w*cmath.exp(-1j*k)
+    matrix[1,0] = v+w*cmath.exp(1j*k)
+    return matrix
+
+
+def main():
+    start_clock = time.perf_counter()
+    delta_1 = 1e-9  # 求导的步长（求导的步长可以尽可能短）
+    delta_2 = 1e-5  # 积分的步长（积分步长和计算时间相关，因此取一个合理值即可）
+    W = 0  # Winding number初始化
+    for k in np.arange(-pi, pi, delta_2):
+        H = hamiltonian(k)
+        log0 = cmath.log(H[0, 1])
+    
+        H_delta = hamiltonian(k+delta_1) 
+        log1 = cmath.log(H_delta[0, 1])
+
+        W = W + (log1-log0)/delta_1*delta_2 # Winding number
+    print('Winding number = ', W/2/pi/1j)
+    end_clock = time.perf_counter()
+    print('CPU执行时间(min)=', (end_clock-start_clock)/60)
+
+
+if __name__ == '__main__':
+    main()

2020.07.26_Hamiltonian_bands_and_Winding_number_in_SSH_model/bands_of_SSH_model.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/5025
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+from math import *  
+import cmath 
+
+
+def hamiltonian(k):  # SSH模型
+    v=0.6
+    w=1
+    matrix = np.zeros((2, 2), dtype=complex)
+    matrix[0,1] = v+w*cmath.exp(-1j*k)
+    matrix[1,0] = v+w*cmath.exp(1j*k)
+    return matrix
+
+
+def main():
+    k = np.linspace(-pi, pi, 100)
+    plot_bands_one_dimension(k, hamiltonian)
+
+
+def plot_bands_one_dimension(k, hamiltonian):
+    dim = hamiltonian(0).shape[0]
+    dim_k = k.shape[0]
+    eigenvalue_k = np.zeros((dim_k, dim))
+    i0 = 0
+    for k0 in k:
+        matrix0 = hamiltonian(k0)
+        eigenvalue, eigenvector = np.linalg.eig(matrix0)
+        eigenvalue_k[i0, :] = np.sort(np.real(eigenvalue[:]))
+        i0 += 1
+    for dim0 in range(dim):
+        plt.plot(k, eigenvalue_k[:, dim0], '-k')
+    plt.show()
+
+
+if __name__ == '__main__':
+    main()