update

2022.07.12_gauge_fixing/example_find_vector_with_fixed_gauge_by_making_one_component_real.py

@@ -3,7 +3,6 @@ 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/22604
 """
 
-
 import numpy as np
 import cmath
 
@@ -25,24 +24,14 @@ def find_vector_with_fixed_gauge_by_making_one_component_real(vector, precision=
 vector_1 = np.array([np.sqrt(0.5), np.sqrt(0.5)])*cmath.exp(np.random.uniform(0, 1)*1j)
 vector_2 = np.array([1, 0])*cmath.exp(np.random.uniform(0, 1)*1j)
 
-print('\n随机规范的原向量：', vector_1)
+print('随机规范的原向量：', vector_1)
+angle = cmath.phase(vector_1[0])
+print('固定规范后的向量（方法1）：', vector_1*cmath.exp(-1j*angle))
 vector_1 = find_vector_with_fixed_gauge_by_making_one_component_real(vector_1, precision=0.001)
-print('固定规范后的向量：', vector_1)
+print('固定规范后的向量（方法2）：', vector_1)
 
 print('\n随机规范的原向量：', vector_2)
+angle = cmath.phase(vector_2[0])
+print('固定规范后的向量（方法1）：', vector_2*cmath.exp(-1j*angle))
 vector_2 = find_vector_with_fixed_gauge_by_making_one_component_real(vector_2, precision=0.001)
-print('固定规范后的向量：', vector_2)
-
-
-# # 可直接使用Guan软件包来调用以上函数：https://py.guanjihuan.com。
-# # 安装命令：pip install --upgrade guan。
-
-# import guan
-
-# print('\n随机规范的原向量：', vector_1)
-# vector_1 = guan.find_vector_with_fixed_gauge_by_making_one_component_real(vector_1, precision=0.001)
-# print('固定规范后的向量：', vector_1)
-
-# print('\n随机规范的原向量：', vector_2)
-# vector_2 = guan.find_vector_with_fixed_gauge_by_making_one_component_real(vector_2, precision=0.001)
-# print('固定规范后的向量：', vector_2)
+print('固定规范后的向量（方法2）：', vector_2)

2022.07.12_gauge_fixing/example_rotation_of_degenerate_vectors.py

@@ -69,10 +69,3 @@ vector1, vector2 = rotation_of_degenerate_vectors(eigenvector[:, 0], eigenvector
 print()
 print(vector1)
 print(vector2, '\n')
-
-
-# # 可直接使用Guan软件包来调用以上函数：https://py.guanjihuan.com。
-# # 安装命令：pip install --upgrade guan。
-# import guan
-# vector1, vector2 = guan.rotation_of_degenerate_vectors(vector1, vector2, index1=None, index2=None, precision=0.01, criterion=0.01, show_theta=0)
-# hamiltonian = guan.hamiltonian_of_bbh_model(kx, ky, gamma_x=0.5, gamma_y=0.5, lambda_x=1, lambda_y=1)

2024.01.25_DOS_with_dyson_equation_2/DOS_with_dyson_equation_2.py

@@ -0,0 +1,63 @@
+"""
+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/38466
+"""
+
+import numpy as np
+
+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_2(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])/np.pi)   # 态密度
+
+def G_ii_n_with_Dyson_equation_2(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):
+        G_nn_n_right_minus = G_11_1
+        G_nn_n_left_minus = G_11_1
+        if i!=0:
+            for _ in range(i-1):
+                G_nn_n_right = Green_nn_n(E, eta, h00, h01, G_nn_n_right_minus)
+                G_nn_n_right_minus = G_nn_n_right
+        if i!=length-1:
+            for _ in range(length-i-2):
+                G_nn_n_left = Green_nn_n(E, eta, h00, h01, G_nn_n_left_minus)
+                G_nn_n_left_minus = G_nn_n_left
+        
+        if i==0:
+            G_ii_n_array[i, :, :] = np.linalg.inv((E+eta*1j)*np.identity(width)-h00-np.dot(np.dot(h01, G_nn_n_left_minus), h01.transpose().conj()))
+        elif i!=0 and i!=length-1:
+            G_ii_n_array[i, :, :] = np.linalg.inv((E+eta*1j)*np.identity(width)-h00-np.dot(np.dot(h01.transpose().conj(), G_nn_n_right_minus), h01)-np.dot(np.dot(h01, G_nn_n_left_minus), h01.transpose().conj()))
+        elif i==length-1: 
+            G_ii_n_array[i, :, :] = np.linalg.inv((E+eta*1j)*np.identity(width)-h00-np.dot(np.dot(h01.transpose().conj(), G_nn_n_right_minus), h01))
+    return G_ii_n_array
+
+def Green_nn_n(E, eta, H00, V, G_nn_n_minus):
+    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
+
+if __name__ == '__main__': 
+    main()