78 lines
3.3 KiB
Python
78 lines
3.3 KiB
Python
"""
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This code is supported by the website: https://www.guanjihuan.com
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The newest version of this code is on the web page: https://www.guanjihuan.com/archives/22604
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"""
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import numpy as np
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import math
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import cmath
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# from numba import jit
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# @jit
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def rotation_of_degenerate_vectors(vector1, vector2, index1=None, index2=None, precision=0.01, criterion=0.01, show_theta=0):
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vector1 = np.array(vector1)
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vector2 = np.array(vector2)
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if index1 == None:
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index1 = np.argmax(np.abs(vector1))
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if index2 == None:
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index2 = np.argmax(np.abs(vector2))
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if np.abs(vector1[index2])>criterion or np.abs(vector2[index1])>criterion:
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for theta in np.arange(0, 2*math.pi, precision):
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if show_theta==1:
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print(theta)
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for phi1 in np.arange(0, 2*math.pi, precision):
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for phi2 in np.arange(0, 2*math.pi, precision):
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vector1_test = cmath.exp(1j*phi1)*vector1*math.cos(theta)+cmath.exp(1j*phi2)*vector2*math.sin(theta)
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vector2_test = -cmath.exp(-1j*phi2)*vector1*math.sin(theta)+cmath.exp(-1j*phi1)*vector2*math.cos(theta)
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if np.abs(vector1_test[index2])<criterion and np.abs(vector2_test[index1])<criterion:
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vector1 = vector1_test
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vector2 = vector2_test
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break
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if np.abs(vector1_test[index2])<criterion and np.abs(vector2_test[index1])<criterion:
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break
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if np.abs(vector1_test[index2])<criterion and np.abs(vector2_test[index1])<criterion:
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break
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return vector1, vector2
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def hamiltonian_of_bbh_model(kx, ky, gamma_x=0.5, gamma_y=0.5, lambda_x=1, lambda_y=1):
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# label of atoms in a unit cell
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# (2) —— (0)
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# | |
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# (1) —— (3)
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hamiltonian = np.zeros((4, 4), dtype=complex)
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hamiltonian[0, 2] = gamma_x+lambda_x*cmath.exp(1j*kx)
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hamiltonian[1, 3] = gamma_x+lambda_x*cmath.exp(-1j*kx)
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hamiltonian[0, 3] = gamma_y+lambda_y*cmath.exp(1j*ky)
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hamiltonian[1, 2] = -gamma_y-lambda_y*cmath.exp(-1j*ky)
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hamiltonian[2, 0] = np.conj(hamiltonian[0, 2])
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hamiltonian[3, 1] = np.conj(hamiltonian[1, 3])
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hamiltonian[3, 0] = np.conj(hamiltonian[0, 3])
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hamiltonian[2, 1] = np.conj(hamiltonian[1, 2])
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return hamiltonian
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# For kx=0
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print('\nFor kx=0:\n')
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eigenvalue, eigenvector = np.linalg.eigh(hamiltonian_of_bbh_model(kx=0, ky=0))
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print(eigenvalue, '\n')
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print(eigenvector[:, 0])
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print(eigenvector[:, 1], '\n')
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# For kx=0.005
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print('\nFor kx=0.005:\n')
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eigenvalue, eigenvector = np.linalg.eigh(hamiltonian_of_bbh_model(kx=0.005, ky=0))
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print(eigenvalue, '\n')
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print(eigenvector[:, 0])
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print(eigenvector[:, 1], '\n\n')
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# Rotaion
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vector1, vector2 = rotation_of_degenerate_vectors(eigenvector[:, 0], eigenvector[:, 1], precision=0.01, criterion=0.01, show_theta=1)
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print()
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print(vector1)
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print(vector2, '\n')
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# # 可直接使用Guan软件包来调用以上函数：https://py.guanjihuan.com。
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# # 安装命令：pip install --upgrade guan。
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# import guan
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# vector1, vector2 = guan.rotation_of_degenerate_vectors(vector1, vector2, index1=None, index2=None, precision=0.01, criterion=0.01, show_theta=0)
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# hamiltonian = guan.hamiltonian_of_bbh_model(kx, ky, gamma_x=0.5, gamma_y=0.5, lambda_x=1, lambda_y=1) |