update

academic_codes/2022.08.12_calculation_of_Chern_number_by_Wilson_loop_for_degenerate_case/calculation_of_Chern_number_by_Wilson_loop_for_degenerate_case.py

@@ -28,6 +28,7 @@ def main():
     Ny = 20
 
     H_k = functools.partial(hamiltonian, Ny=Ny, B=1/Ny)
+    
     chern_number = calculate_chern_number_for_square_lattice_with_wilson_loop_for_degenerate_case(H_k, index_of_bands=range(int(Ny/2)-1), precision_of_wilson_loop=5)
     print('价带：', chern_number)
     print()

academic_codes/2022.08.28_calculation_of_Chern_number_by_efficient_method_for_degenerate_case/calculation_of_Chern_number_by_efficient_method_for_degenerate_case.py

@@ -0,0 +1,116 @@
+"""
+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/25107
+"""
+
+import numpy as np
+import math
+from math import *
+import cmath
+import functools
+
+
+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 = 20
+
+    H_k = functools.partial(hamiltonian, Ny=Ny, B=1/Ny)
+
+    chern_number = calculate_chern_number_for_square_lattice_with_efficient_method_for_degenerate_case(H_k, index_of_bands=range(int(Ny/2)-1))
+    print('价带：', chern_number)
+    print()
+
+    chern_number = calculate_chern_number_for_square_lattice_with_efficient_method_for_degenerate_case(H_k, index_of_bands=range(int(Ny/2)+2))
+    print('价带（包含两个交叉能带）：', chern_number)
+    print()
+
+    chern_number = calculate_chern_number_for_square_lattice_with_efficient_method_for_degenerate_case(H_k, index_of_bands=range(Ny))
+    print('所有能带：', chern_number)
+
+    # 函数可通过Guan软件包调用。安装方法：pip install --upgrade guan
+    # import guan
+    # chern_number = guan.calculate_chern_number_for_square_lattice_with_efficient_method_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], precision=100, print_show=0)
+
+
+def calculate_chern_number_for_square_lattice_with_efficient_method_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], precision=100, print_show=0): 
+    delta = 2*math.pi/precision
+    chern_number = 0
+    for kx in np.arange(-math.pi, math.pi, delta):
+        if print_show == 1:
+            print(kx)
+        for ky in np.arange(-math.pi, math.pi, delta):
+            H = hamiltonian_function(kx, ky)
+            eigenvalue, vector = np.linalg.eigh(H) 
+            H_delta_kx = hamiltonian_function(kx+delta, ky) 
+            eigenvalue, vector_delta_kx = np.linalg.eigh(H_delta_kx) 
+            H_delta_ky = hamiltonian_function(kx, ky+delta)
+            eigenvalue, vector_delta_ky = np.linalg.eigh(H_delta_ky) 
+            H_delta_kx_ky = hamiltonian_function(kx+delta, ky+delta)
+            eigenvalue, vector_delta_kx_ky = np.linalg.eigh(H_delta_kx_ky)
+            dim = len(index_of_bands)
+            det_value = 1
+            # first dot
+            dot_matrix = np.zeros((dim , dim), dtype=complex)
+            i0 = 0
+            for dim1 in index_of_bands:
+                j0 = 0
+                for dim2 in index_of_bands:
+                    dot_matrix[dim1, dim2] = np.dot(np.conj(vector[:, dim1]), vector_delta_kx[:, dim2])
+                    j0 += 1
+                i0 += 1
+            dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
+            det_value = det_value*dot_matrix
+            # second dot
+            dot_matrix = np.zeros((dim , dim), dtype=complex)
+            i0 = 0
+            for dim1 in index_of_bands:
+                j0 = 0
+                for dim2 in index_of_bands:
+                    dot_matrix[dim1, dim2] = np.dot(np.conj(vector_delta_kx[:, dim1]), vector_delta_kx_ky[:, dim2])
+                    j0 += 1
+                i0 += 1
+            dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
+            det_value = det_value*dot_matrix
+            # third dot
+            dot_matrix = np.zeros((dim , dim), dtype=complex)
+            i0 = 0
+            for dim1 in index_of_bands:
+                j0 = 0
+                for dim2 in index_of_bands:
+                    dot_matrix[dim1, dim2] = np.dot(np.conj(vector_delta_kx_ky[:, dim1]), vector_delta_ky[:, dim2])
+                    j0 += 1
+                i0 += 1
+            dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
+            det_value = det_value*dot_matrix
+            # four dot
+            dot_matrix = np.zeros((dim , dim), dtype=complex)
+            i0 = 0
+            for dim1 in index_of_bands:
+                j0 = 0
+                for dim2 in index_of_bands:
+                    dot_matrix[dim1, dim2] = np.dot(np.conj(vector_delta_ky[:, dim1]), vector[:, dim2])
+                    j0 += 1
+                i0 += 1
+            dot_matrix = np.linalg.det(dot_matrix)/abs(np.linalg.det(dot_matrix))
+            det_value= det_value*dot_matrix
+            chern_number += cmath.log(det_value)
+    chern_number = chern_number/(2*math.pi*1j)
+    return chern_number
+
+
+if __name__ == '__main__':
+    main()