Create local_Chern_marker_of_half_BHZ_model.py

2024.08.19_local_Chern_marker_of_half_BHZ_model/local_Chern_marker_of_half_BHZ_model.py

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+import numpy as np
+import guan
+
+
+# 计算投影算符
+def compute_projection_operator(Ny, Nx):
+    H0, H1, H2 = guan.get_onsite_and_hopping_terms_of_half_bhz_model_for_spin_down(A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, M=-0.01, a=1)
+    hamiltonian = guan.hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(N1=Ny, N2=Nx, on_site=H0, hopping_1=H1, hopping_2=H2, period_1=0, period_2=0)
+
+    P = np.zeros((2*Ny*Nx, 2*Ny*Nx), dtype=complex)
+    eigenvalue, eigenvector = np.linalg.eigh(hamiltonian)
+    occupied = 0
+    for i0 in eigenvalue:
+        if i0 <= 0:
+            occupied += 1
+    for i0 in range(occupied):
+        P += np.outer(eigenvector[:, i0], eigenvector[:, i0].conj())
+    
+    return P
+
+
+# 计算local Chern marker
+def compute_local_chern_marker(Ny, Nx, P):
+    C_local = np.zeros((Ny, Nx), dtype=complex)
+    x_array = np.zeros((2*Ny*Nx))
+    y_array = np.zeros((2*Ny*Nx))
+    for iy in range(Ny):
+        for ix in range(Nx):
+            x_array[2*Nx*iy + 2*ix + 0] = ix
+            x_array[2*Nx*iy + 2*ix + 1] = ix
+            y_array[2*Nx*iy + 2*ix + 0] = iy
+            y_array[2*Nx*iy + 2*ix + 1] = iy
+    x_matrix = np.diag(x_array)   
+    y_matrix = np.diag(y_array) 
+
+    PxP = P @ x_matrix @ P
+    PyP = P @ y_matrix @ P
+    commutator = PxP @ PyP - PyP @ PxP
+    for iy in range(Ny):
+        for ix in range(Nx):
+            C_local[iy, ix] = -2 * np.pi * 1j * (commutator[2*Nx*iy+ 2*ix + 0, 2*Nx*iy+ 2*ix + 0] + commutator[2*Nx*iy+ 2*ix + 1, 2*Nx*iy+ 2*ix + 1])
+
+    # # 或者用这个
+    # temp = 4 * np.pi * np.imag(P @ x_matrix @ P @ y_matrix @ P)
+    # for iy in range(Ny):
+    #     for ix in range(Nx):
+    #         C_local[iy, ix] = temp[2*Nx*iy + 2*ix + 0, 2*Nx*iy + 2*ix + 0] + temp[2*Nx*iy + 2*ix + 1, 2*Nx*iy + 2*ix + 1]
+
+    return C_local.real
+
+
+Nx=30
+Ny=30
+P = compute_projection_operator(Ny, Nx)
+C_local = compute_local_chern_marker(Ny, Nx, P)
+guan.plot_pcolor(range(Nx), range(Ny), C_local, cmap='RdBu')