update

2020.01.03_bands_of_qusi_1D_square_lattice/bands_of_qusi_1D_square_lattice.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/3895
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+from math import *
+import cmath
+import functools
+
+
+def hamiltonian(k, N, t):  # 准一维方格子哈密顿量
+    # 初始化为零矩阵
+    h00 = np.zeros((N, N), dtype=complex)
+    h01 = np.zeros((N, N), dtype=complex)
+    for i in range(N-1):   # 原胞内的跃迁h00
+        h00[i, i+1] = t
+        h00[i+1, i] = t
+    for i in range(N):   # 原胞间的跃迁h01
+        h01[i, i] = t
+    matrix = h00 + h01*cmath.exp(1j*k) + h01.transpose().conj()*cmath.exp(-1j*k)
+    return matrix
+
+
+def main():
+    H_k = functools.partial(hamiltonian, N=10, t=1)
+    k = np.linspace(-pi, pi, 300)
+    plot_bands_one_dimension(k, H_k)
+
+
+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()