38 lines
1.9 KiB
Python
38 lines
1.9 KiB
Python
# calculate Chern number
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import numpy as np
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import cmath
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from math import *
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from .calculate_wave_functions import *
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def calculate_chern_number_for_square_lattice(hamiltonian_function, precision=100):
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if np.array(hamiltonian_function(0, 0)).shape==():
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dim = 1
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else:
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dim = np.array(hamiltonian_function(0, 0)).shape[0]
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delta = 2*pi/precision
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chern_number = np.zeros(dim, dtype=complex)
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for kx in np.arange(-pi, pi, delta):
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for ky in np.arange(-pi, pi, delta):
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H = hamiltonian_function(kx, ky)
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vector = calculate_eigenvector(H)
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H_delta_kx = hamiltonian_function(kx+delta, ky)
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vector_delta_kx = calculate_eigenvector(H_delta_kx)
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H_delta_ky = hamiltonian_function(kx, ky+delta)
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vector_delta_ky = calculate_eigenvector(H_delta_ky)
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H_delta_kx_ky = hamiltonian_function(kx+delta, ky+delta)
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vector_delta_kx_ky = calculate_eigenvector(H_delta_kx_ky)
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for i in range(dim):
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vector_i = vector[:, i]
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vector_delta_kx_i = vector_delta_kx[:, i]
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vector_delta_ky_i = vector_delta_ky[:, i]
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vector_delta_kx_ky_i = vector_delta_kx_ky[:, i]
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Ux = np.dot(np.conj(vector_i), vector_delta_kx_i)/abs(np.dot(np.conj(vector_i), vector_delta_kx_i))
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Uy = np.dot(np.conj(vector_i), vector_delta_ky_i)/abs(np.dot(np.conj(vector_i), vector_delta_ky_i))
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Ux_y = np.dot(np.conj(vector_delta_ky_i), vector_delta_kx_ky_i)/abs(np.dot(np.conj(vector_delta_ky_i), vector_delta_kx_ky_i))
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Uy_x = np.dot(np.conj(vector_delta_kx_i), vector_delta_kx_ky_i)/abs(np.dot(np.conj(vector_delta_kx_i), vector_delta_kx_ky_i))
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F = cmath.log(Ux*Uy_x*(1/Ux_y)*(1/Uy))
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chern_number[i] = chern_number[i] + F
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chern_number = chern_number/(2*pi*1j)
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return chern_number
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