update

2020.12.31_DOS_calculation_using_Dyson_equations/square_lattice/DOS_calculation_using_Dyson_equations_in_square_lattice.py

@@ -0,0 +1,95 @@
+"""
+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/7650
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+from math import *
+
+
+def matrix_00(width):  
+    h00 = np.zeros((width, width))
+    for width0 in range(width-1):
+        h00[width0, width0+1] = 1
+        h00[width0+1, width0] = 1
+    return h00
+
+
+def matrix_01(width): 
+    h01 = np.identity(width)
+    return h01
+    
+
+def main():
+    width = 2
+    length = 3
+    eta = 1e-2
+    E = 0
+    h00 = matrix_00(width)
+    h01 = matrix_01(width)
+    G_ii_n_array = G_ii_n_with_Dyson_equation(width, length, E, eta, h00, h01)
+    for i0 in range(length):
+        # print('G_{'+str(i0+1)+','+str(i0+1)+'}^{('+str(length)+')}:')
+        # print(G_ii_n_array[i0, :, :],'\n')
+        print('x=', i0+1, ':')
+        for j0 in range(width):
+            print('     y=', j0+1, ' ', -np.imag(G_ii_n_array[i0, j0, j0])/pi)   # 态密度
+
+
+def G_ii_n_with_Dyson_equation(width, length, E, eta, h00, h01):
+    G_ii_n_array = np.zeros((length, width, width), complex)
+    G_11_1 = np.linalg.inv((E+eta*1j)*np.identity(width)-h00)
+    for i in range(length):  # i为格林函数的右下指标
+        # 初始化开始
+        G_nn_n_minus = G_11_1
+        G_in_n_minus = G_11_1
+        G_ni_n_minus = G_11_1
+        G_ii_n_minus = G_11_1
+        for i0 in range(i):
+            G_nn_n = Green_nn_n(E, eta, h00, h01, G_nn_n_minus)
+            G_nn_n_minus = G_nn_n
+        if i!=0:
+            G_in_n_minus = G_nn_n
+            G_ni_n_minus = G_nn_n
+            G_ii_n_minus = G_nn_n
+        # 初始化结束
+        for j0 in range(length-1-i): # j0为格林函数的右上指标，表示当前体系大小，即G^{(j0)}
+            G_nn_n = Green_nn_n(E, eta, h00, h01, G_nn_n_minus)
+            G_nn_n_minus = G_nn_n
+
+            G_ii_n = Green_ii_n(G_ii_n_minus, G_in_n_minus, h01, G_nn_n, G_ni_n_minus)  # 需要求的对角分块矩阵
+            G_ii_n_minus = G_ii_n
+
+            G_in_n = Green_in_n(G_in_n_minus, h01, G_nn_n)
+            G_in_n_minus = G_in_n
+
+            G_ni_n = Green_ni_n(G_nn_n, h01, G_ni_n_minus)
+            G_ni_n_minus = G_ni_n
+        G_ii_n_array[i, :, :] = G_ii_n_minus
+    return G_ii_n_array
+
+
+def Green_nn_n(E, eta, H00, V, G_nn_n_minus): # n>=2
+    dim  = H00.shape[0]
+    G_nn_n = np.linalg.inv((E+eta*1j)*np.identity(dim)-H00-np.dot(np.dot(V.transpose().conj(), G_nn_n_minus), V))
+    return G_nn_n
+
+
+def Green_in_n(G_in_n_minus, V, G_nn_n):  # n>=2
+    G_in_n = np.dot(np.dot(G_in_n_minus, V), G_nn_n)
+    return G_in_n
+
+
+def Green_ni_n(G_nn_n, V, G_ni_n_minus): # n>=2
+    G_ni_n = np.dot(np.dot(G_nn_n, V.transpose().conj()), G_ni_n_minus)
+    return G_ni_n
+
+
+def Green_ii_n(G_ii_n_minus, G_in_n_minus, V, G_nn_n, G_ni_n_minus):  # n>=i
+    G_ii_n = G_ii_n_minus+np.dot(np.dot(np.dot(np.dot(G_in_n_minus, V), G_nn_n), V.transpose().conj()),G_ni_n_minus)
+    return G_ii_n
+
+
+if __name__ == '__main__': 
+    main()

2020.12.31_DOS_calculation_using_Dyson_equations/square_lattice/get_DOS_by_direct_inverseion_of_Hamiltonian_of_square_lattice.py

@@ -0,0 +1,41 @@
+"""
+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/7650
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+from math import *
+
+
+def hamiltonian(width, length):  
+    h = np.zeros((width*length, width*length))
+    for i0 in range(length):
+        for j0 in range(width-1):
+            h[i0*width+j0, i0*width+j0+1] = 1
+            h[i0*width+j0+1, i0*width+j0] = 1
+    for i0 in range(length-1):
+        for j0 in range(width):
+            h[i0*width+j0, (i0+1)*width+j0] = 1
+            h[(i0+1)*width+j0, i0*width+j0] = 1
+    return h
+
+
+def main():
+    width = 2
+    length = 3
+    h = hamiltonian(width, length)
+    E = 0
+    green = np.linalg.inv((E+1e-2j)*np.eye(width*length)-h)  
+    for i0 in range(length):
+        # print('G_{'+str(i0+1)+','+str(i0+1)+'}^{('+str(length)+')}:')
+        # print(green[i0*width+0: i0*width+width, i0*width+0: i0*width+width], '\n') 
+        print('x=', i0+1, ':')
+        for j0 in range(width):
+            print('     y=', j0+1, ' ', -np.imag(green[i0*width+j0, i0*width+j0])/pi) 
+
+
+if __name__ == "__main__":
+    main()
+
+