diff --git a/academic_codes/2021.12.28_calculation_of_Chern_number_by_Wilson_loop/calculation_of_Chern_number_by_Wilson_loop.py b/academic_codes/2021.12.28_calculation_of_Chern_number_by_Wilson_loop/calculation_of_Chern_number_by_Wilson_loop.py index 4b3094f..137bdc9 100644 --- a/academic_codes/2021.12.28_calculation_of_Chern_number_by_Wilson_loop/calculation_of_Chern_number_by_Wilson_loop.py +++ b/academic_codes/2021.12.28_calculation_of_Chern_number_by_Wilson_loop/calculation_of_Chern_number_by_Wilson_loop.py @@ -24,39 +24,48 @@ def hamiltonian(kx, ky): # 量子反常霍尔QAH模型（该参数对应的陈 def main(): start_time = time.time() - n = 100 # 积分密度 - delta = 2*pi/n + n1 = 10 # small plaquettes精度 + n2 = 800 # Wilson loop精度 + delta = 2*pi/n1 chern_number = 0 for kx in np.arange(-pi, pi, delta): for ky in np.arange(-pi, pi, delta): - H = hamiltonian(kx, ky) - eigenvalue, eigenvector = np.linalg.eig(H) - vector = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] # 价带波函数 - # vector = eigenvector[:, np.argsort(np.real(eigenvalue))[0]]*cmath.exp(1j*np.random.uniform(0, pi)) # 验证规范不依赖性 - - H_delta_kx = hamiltonian(kx+delta, ky) - eigenvalue, eigenvector = np.linalg.eig(H_delta_kx) - vector_delta_kx = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] # 略偏离kx的波函数 - - H_delta_ky = hamiltonian(kx, ky+delta) - eigenvalue, eigenvector = np.linalg.eig(H_delta_ky) - vector_delta_ky = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] # 略偏离ky的波函数 - - H_delta_kx_ky = hamiltonian(kx+delta, ky+delta) - eigenvalue, eigenvector = np.linalg.eig(H_delta_kx_ky) - vector_delta_kx_ky = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] # 略偏离kx和ky的波函数 - - line_1 = np.dot(vector.transpose().conj(), vector_delta_kx) - line_2 = np.dot(vector_delta_kx.transpose().conj(), vector_delta_kx_ky) - line_3 = np.dot(vector_delta_kx_ky.transpose().conj(), vector_delta_ky) - line_4 = np.dot(vector_delta_ky.transpose().conj(), vector) - - arg = np.log(np.dot(np.dot(np.dot(line_1, line_2), line_3), line_4))/1j + vector_array = [] + # line_1 + for i2 in range(n2+1): + H_delta = hamiltonian(kx+delta/n2*i2, ky) + eigenvalue, eigenvector = np.linalg.eig(H_delta) + vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] + # vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))[0]]*cmath.exp(1j*np.random.uniform(0, pi)) # 验证规范不依赖性 + vector_array.append(vector_delta) + # line_2 + for i2 in range(n2): + H_delta = hamiltonian(kx+delta, ky+delta/n2*(i2+1)) + eigenvalue, eigenvector = np.linalg.eig(H_delta) + vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] + vector_array.append(vector_delta) + # line_3 + for i2 in range(n2): + H_delta = hamiltonian(kx+delta-delta/n2*(i2+1), ky+delta) + eigenvalue, eigenvector = np.linalg.eig(H_delta) + vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] + vector_array.append(vector_delta) + # line_4 + for i2 in range(n2-1): + H_delta = hamiltonian(kx, ky+delta-delta/n2*(i2+1)) + eigenvalue, eigenvector = np.linalg.eig(H_delta) + vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] + vector_array.append(vector_delta) + Wilson_loop = 1 + for i0 in range(len(vector_array)-1): + Wilson_loop = Wilson_loop*np.dot(vector_array[i0].transpose().conj(), vector_array[i0+1]) + Wilson_loop = Wilson_loop*np.dot(vector_array[len(vector_array)-1].transpose().conj(), vector_array[0]) + arg = np.log(Wilson_loop)/1j chern_number = chern_number + arg chern_number = chern_number/(2*pi) print('Chern number = ', chern_number) end_time = time.time() - print('运行时间(min)=', (end_time-start_time)/60) + print('运行时间（秒）=', end_time-start_time) if __name__ == '__main__': diff --git a/academic_codes/2021.12.28_calculation_of_Chern_number_by_Wilson_loop/calculation_of_Chern_number_by_Wilson_loop_(wrong).py b/academic_codes/2021.12.28_calculation_of_Chern_number_by_Wilson_loop/calculation_of_Chern_number_by_Wilson_loop_(wrong).py new file mode 100644 index 0000000..166007e --- /dev/null +++ b/academic_codes/2021.12.28_calculation_of_Chern_number_by_Wilson_loop/calculation_of_Chern_number_by_Wilson_loop_(wrong).py @@ -0,0 +1,67 @@ +""" +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/18319 +""" + +""" +Notice that this code is not correct for calculating the Chern number because of the low precision in the calculation of Wilson loop! +""" + +import numpy as np +from math import * +import time +import cmath + + +def hamiltonian(kx, ky): # 量子反常霍尔QAH模型（该参数对应的陈数为2） + t1 = 1.0 + t2 = 1.0 + t3 = 0.5 + m = -1.0 + matrix = np.zeros((2, 2), dtype=complex) + matrix[0, 1] = 2*t1*cos(kx)-1j*2*t1*cos(ky) + matrix[1, 0] = 2*t1*cos(kx)+1j*2*t1*cos(ky) + matrix[0, 0] = m+2*t3*sin(kx)+2*t3*sin(ky)+2*t2*cos(kx+ky) + matrix[1, 1] = -(m+2*t3*sin(kx)+2*t3*sin(ky)+2*t2*cos(kx+ky)) + return matrix + + +def main(): + start_time = time.time() + n = 200 # 积分密度 + delta = 2*pi/n + chern_number = 0 + for kx in np.arange(-pi, pi, delta): + for ky in np.arange(-pi, pi, delta): + H = hamiltonian(kx, ky) + eigenvalue, eigenvector = np.linalg.eig(H) + vector = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] # 价带波函数 + # vector = eigenvector[:, np.argsort(np.real(eigenvalue))[0]]*cmath.exp(1j*np.random.uniform(0, pi)) # 验证规范不依赖性 + + H_delta_kx = hamiltonian(kx+delta, ky) + eigenvalue, eigenvector = np.linalg.eig(H_delta_kx) + vector_delta_kx = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] # 略偏离kx的波函数 + + H_delta_ky = hamiltonian(kx, ky+delta) + eigenvalue, eigenvector = np.linalg.eig(H_delta_ky) + vector_delta_ky = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] # 略偏离ky的波函数 + + H_delta_kx_ky = hamiltonian(kx+delta, ky+delta) + eigenvalue, eigenvector = np.linalg.eig(H_delta_kx_ky) + vector_delta_kx_ky = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] # 略偏离kx和ky的波函数 + + line_1 = np.dot(vector.transpose().conj(), vector_delta_kx) + line_2 = np.dot(vector_delta_kx.transpose().conj(), vector_delta_kx_ky) + line_3 = np.dot(vector_delta_kx_ky.transpose().conj(), vector_delta_ky) + line_4 = np.dot(vector_delta_ky.transpose().conj(), vector) + + arg = np.log(np.dot(np.dot(np.dot(line_1, line_2), line_3), line_4))/1j + chern_number = chern_number + arg + chern_number = chern_number/(2*pi) + print('Chern number = ', chern_number) + end_time = time.time() + print('运行时间（秒）=', end_time-start_time) + + +if __name__ == '__main__': + main() \ No newline at end of file