update

2021.01.07_Hofstadter_butterfly_in_square_lattice/Hofstadter_butterfly_in_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/8491
+"""
+
+import numpy as np
+import cmath
+import matplotlib.pyplot as plt
+
+
+def main():
+    for n in np.arange(1, 11):
+        print('n=', n)
+        width = n
+        length = n
+        B_array = np.arange(0, 1, 0.001)
+        eigenvalue_all = np.zeros((B_array.shape[0], width*length))
+        i0 = 0
+        for B in B_array:
+            # print(B)
+            h = hamiltonian(width, length, B)
+            eigenvalue, eigenvector = np.linalg.eig(h)
+            eigenvalue_all[i0, :] = np.real(eigenvalue)
+            i0 += 1
+        plt.plot(B_array, eigenvalue_all, '.r', markersize=0.5)
+        plt.title('width=length='+str(n))
+        plt.xlabel('B*a^2/phi_0')
+        plt.ylabel('E')
+        plt.savefig('width=length='+str(n)+'.jpg', dpi=300)
+        plt.close('all')  # 关闭所有plt，防止循环画图时占用内存
+        # plt.show()
+
+
+def hamiltonian(width, length, B):   # 方格子哈密顿量
+    h = np.zeros((width*length, width*length), dtype=complex)
+    # y方向的跃迁
+    for x in range(length):
+        for y in range(width-1):
+            h[x*width+y, x*width+y+1] = 1
+            h[x*width+y+1, x*width+y] = 1
+    # x方向的跃迁
+    for x in range(length-1):
+        for y in range(width):
+            h[x*width+y, (x+1)*width+y] = 1*cmath.exp(-2*np.pi*1j*B*y)
+            h[(x+1)*width+y, x*width+y] = 1*cmath.exp(2*np.pi*1j*B*y)
+    return h
+
+
+if __name__ == "__main__":
+    main()