update

academic_codes/2021.01.07_Hofstadter_butterfly_in_square_lattice/Hofstadter_butterfly_in_square_lattice.py

@@ -32,7 +32,7 @@ def main():
 
 
 def hamiltonian(width, length, B):   # 方格子哈密顿量
-    h = np.zeros((width*length, width*length))*(1+0j)
+    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):

academic_codes/2021.12.27_Chern_numbers_of_Landau_levels/Chern_numbers_of_Landau_levels_in_honeycomb_lattice.py

@@ -0,0 +1,57 @@
+"""
+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/18306
+"""
+
+import numpy as np
+from math import *
+import cmath
+import functools
+import guan
+
+
+def hamiltonian(kx, ky, Ny, a, B):
+    h00 = np.zeros((4*Ny, 4*Ny), dtype=complex)
+    h01 = np.zeros((4*Ny, 4*Ny), dtype=complex)
+    t1= 1
+    M = 0
+    for i in range(Ny):
+        h00[i*4+0, i*4+0] = M
+        h00[i*4+1, i*4+1] = -M
+        h00[i*4+2, i*4+2] = M
+        h00[i*4+3, i*4+3] = -M
+        h00[i*4+0, i*4+1] = t1*cmath.exp(-2*pi*1j*B*(3*a*i+1/4*a)*(np.sqrt(3)/2*a))
+        h00[i*4+1, i*4+0] = np.conj(h00[i*4+0, i*4+1])
+        h00[i*4+1, i*4+2] = t1
+        h00[i*4+2, i*4+1] = np.conj(h00[i*4+1, i*4+2])
+        h00[i*4+2, i*4+3] = t1*cmath.exp(2*pi*1j*B*(3*a*i+7/4*a)*(np.sqrt(3)/2)*a)
+        h00[i*4+3, i*4+2] = np.conj(h00[i*4+2, i*4+3])
+    for i in range(Ny-1):
+        h00[i*4+3, (i+1)*4+0] = t1
+        h00[(i+1)*4+0, i*4+3] = t1
+    h00[(Ny-1)*4+3, 0+0] = t1*cmath.exp(1j*ky)
+    h00[0+0, (Ny-1)*4+3] = t1*cmath.exp(-1j*ky)
+    for i in range(Ny):
+        h01[i*4+1, i*4+0] = t1*cmath.exp(-2*pi*1j*B*(3*a*i+1/4*a)*(np.sqrt(3)/2*a))
+        h01[i*4+2, i*4+3] = t1*cmath.exp(-2*pi*1j*B*(3*a*i+7/4*a)*(np.sqrt(3)/2*a))
+    matrix = h00 + h01*cmath.exp(1j*kx) + h01.transpose().conj()*cmath.exp(-1j*kx)
+    return matrix
+
+
+def main():
+    Ny = 10
+    a = 1
+
+    k_array = np.linspace(-pi, pi, 100)
+    H_k = functools.partial(hamiltonian, ky=0, Ny=Ny, a=a, B=1/(3*a*Ny))
+    eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, H_k)
+    guan.plot(k_array, eigenvalue_array, xlabel='kx', ylabel='E', type='k')
+
+    H_k = functools.partial(hamiltonian, Ny=Ny, a=a, B=1/(3*a*Ny))
+    chern_number = guan.calculate_chern_number_for_square_lattice(H_k, precision=100)
+    print(chern_number)
+    print(sum(chern_number))
+
+
+if __name__ == '__main__':
+    main()

academic_codes/2021.12.27_Chern_numbers_of_Landau_levels/Chern_numbers_of_Landau_levels_in_square_lattice.py

@@ -0,0 +1,42 @@
+"""
+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/18306
+"""
+
+import numpy as np
+from math import *
+import cmath
+import functools
+import guan
+
+def hamiltonian(kx, ky, Ny, B):
+    h00 = np.zeros((Ny, Ny), dtype=complex)
+    h01 = np.zeros((Ny, Ny), dtype=complex)
+    t = 1
+    for iy in range(Ny-1):
+        h00[iy, iy+1] = t
+        h00[iy+1, iy] = t
+    h00[Ny-1, 0] = t*cmath.exp(1j*ky)
+    h00[0, Ny-1] = t*cmath.exp(-1j*ky)
+    for iy in range(Ny):
+        h01[iy, iy] = t*cmath.exp(-2*np.pi*1j*B*iy)
+    matrix = h00 + h01*cmath.exp(1j*kx) + h01.transpose().conj()*cmath.exp(-1j*kx)
+    return matrix
+
+
+def main():
+    Ny = 40
+
+    k_array = np.linspace(-pi, pi, 100)
+    H_k = functools.partial(hamiltonian, ky=0, Ny=Ny, B=1/Ny)
+    eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, H_k)
+    guan.plot(k_array, eigenvalue_array, xlabel='kx', ylabel='E', type='k')
+
+    H_k = functools.partial(hamiltonian, Ny=Ny, B=1/Ny)
+    chern_number = guan.calculate_chern_number_for_square_lattice(H_k, precision=100)
+    print(chern_number)
+    print(sum(chern_number))
+
+
+if __name__ == '__main__':
+    main()