diff --git a/academic_codes/2020.11.27_find_the_same_gauge_numerically_by_binary_search/function_form.py b/academic_codes/2020.11.27_find_the_same_gauge_numerically_by_binary_search/function_form.py deleted file mode 100755 index 9d1acdd..0000000 --- a/academic_codes/2020.11.27_find_the_same_gauge_numerically_by_binary_search/function_form.py +++ /dev/null @@ -1,39 +0,0 @@ -""" -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/7516 -""" - -def find_vector_with_the_same_gauge(vector_1, vector_0): - # 寻找近似的同一的规范 - phase_1_pre = 0 - phase_2_pre = pi - n_test = 10001 - for i0 in range(n_test): - test_1 = np.sum(np.abs(vector_1*cmath.exp(1j*phase_1_pre) - vector_0)) - test_2 = np.sum(np.abs(vector_1*cmath.exp(1j*phase_2_pre) - vector_0)) - if test_1 < 1e-6: - phase = phase_1_pre - # print('Done with i0=', i0) - break - if i0 == n_test-1: - phase = phase_1_pre - print('Gauge Not Found with i0=', i0) - if test_1 < test_2: - if i0 == 0: - phase_1 = phase_1_pre-(phase_2_pre-phase_1_pre)/2 - phase_2 = phase_1_pre+(phase_2_pre-phase_1_pre)/2 - else: - phase_1 = phase_1_pre - phase_2 = phase_1_pre+(phase_2_pre-phase_1_pre)/2 - else: - if i0 == 0: - phase_1 = phase_2_pre-(phase_2_pre-phase_1_pre)/2 - phase_2 = phase_2_pre+(phase_2_pre-phase_1_pre)/2 - else: - phase_1 = phase_2_pre-(phase_2_pre-phase_1_pre)/2 - phase_2 = phase_2_pre - phase_1_pre = phase_1 - phase_2_pre = phase_2 - vector_1 = vector_1*cmath.exp(1j*phase) - # print('二分查找找到的规范=', phase) - return vector_1 \ No newline at end of file diff --git a/academic_codes/2020.11.27_find_the_same_gauge_numerically_by_binary_search/find_the_same_gauge_numerically_by_binary_search.py b/academic_codes/2020.11.27_find_the_same_gauge_numerically_with_binary_search/find_the_same_gauge_numerically_with_binary_search.py old mode 100755 new mode 100644 similarity index 97% rename from academic_codes/2020.11.27_find_the_same_gauge_numerically_by_binary_search/find_the_same_gauge_numerically_by_binary_search.py rename to academic_codes/2020.11.27_find_the_same_gauge_numerically_with_binary_search/find_the_same_gauge_numerically_with_binary_search.py index 7ef9ebd..53cc6cc --- a/academic_codes/2020.11.27_find_the_same_gauge_numerically_by_binary_search/find_the_same_gauge_numerically_by_binary_search.py +++ b/academic_codes/2020.11.27_find_the_same_gauge_numerically_with_binary_search/find_the_same_gauge_numerically_with_binary_search.py @@ -1,114 +1,113 @@ -""" -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/7516 -""" - -import numpy as np -import matplotlib.pyplot as plt -from math import * # 引入pi, cos等 -import cmath -import time - - -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))*(1+0j) - 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 = 100 # 积分密度 - delta = 1e-9 # 求导的偏离量 - chern_number = 0 # 陈数初始化 - for kx in np.arange(-pi, pi, 2*pi/n): - for ky in np.arange(-pi, pi, 2*pi/n): - H = hamiltonian(kx, ky) - eigenvalue, eigenvector = np.linalg.eig(H) - vector = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] # 价带波函数 - - 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 - - # vector = vector*cmath.exp(-1j*1) - # vector_delta_kx = vector_delta_kx*cmath.exp(-1j*1) - # vector_delta_ky = vector_delta_ky*cmath.exp(-1j*1) - # vector_delta_kx_ky = vector_delta_kx_ky*cmath.exp(-1j*(1+1e-8)) - - - rand = np.random.uniform(-pi, pi) - vector_delta_kx_ky = vector_delta_kx_ky*cmath.exp(-1j*rand) - - # 寻找近似的同一的规范 - phase_1_pre = 0 - phase_2_pre = pi - n_test = 10001 - for i0 in range(n_test): - test_1 = np.sum(np.abs(vector_delta_kx_ky*cmath.exp(1j*phase_1_pre) - vector)) - test_2 = np.sum(np.abs(vector_delta_kx_ky*cmath.exp(1j*phase_2_pre) - vector)) - if test_1 < 1e-6: - phase = phase_1_pre - print('Done with i0=', i0) - break - if i0 == n_test-1: - phase = phase_1_pre - print('Not Found with i0=', i0) - if test_1 < test_2: - if i0 == 0: - phase_1 = phase_1_pre-(phase_2_pre-phase_1_pre)/2 - phase_2 = phase_1_pre+(phase_2_pre-phase_1_pre)/2 - else: - phase_1 = phase_1_pre - phase_2 = phase_1_pre+(phase_2_pre-phase_1_pre)/2 - else: - if i0 == 0: - phase_1 = phase_2_pre-(phase_2_pre-phase_1_pre)/2 - phase_2 = phase_2_pre+(phase_2_pre-phase_1_pre)/2 - else: - phase_1 = phase_2_pre-(phase_2_pre-phase_1_pre)/2 - phase_2 = phase_2_pre - phase_1_pre = phase_1 - phase_2_pre = phase_2 - - vector_delta_kx_ky = vector_delta_kx_ky*cmath.exp(1j*phase) - print('随机的规范=', rand) # 可注释掉 - print('二分查找找到的规范=', phase) # 可注释掉 - print() # 可注释掉 - - - # 价带的波函数的贝里联络(berry connection) # 求导后内积 - A_x = np.dot(vector.transpose().conj(), (vector_delta_kx-vector)/delta) # 贝里联络Ax（x分量） - A_y = np.dot(vector.transpose().conj(), (vector_delta_ky-vector)/delta) # 贝里联络Ay（y分量） - - A_x_delta_ky = np.dot(vector_delta_ky.transpose().conj(), (vector_delta_kx_ky-vector_delta_ky)/delta) # 略偏离ky的贝里联络Ax - A_y_delta_kx = np.dot(vector_delta_kx.transpose().conj(), (vector_delta_kx_ky-vector_delta_kx)/delta) # 略偏离kx的贝里联络Ay - - # 贝里曲率(berry curvature) - F = (A_y_delta_kx-A_y)/delta-(A_x_delta_ky-A_x)/delta - - # 陈数(chern number) - chern_number = chern_number + F*(2*pi/n)**2 - chern_number = chern_number/(2*pi*1j) - print('Chern number = ', chern_number) - end_time = time.time() - print('运行时间(min)=', (end_time-start_time)/60) - - -if __name__ == '__main__': - main() +""" +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/7516 +""" + +import numpy as np +from math import * # 引入pi, cos等 +import cmath +import time + + +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))*(1+0j) + 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 = 100 # 积分密度 + delta = 1e-9 # 求导的偏离量 + chern_number = 0 # 陈数初始化 + for kx in np.arange(-pi, pi, 2*pi/n): + for ky in np.arange(-pi, pi, 2*pi/n): + H = hamiltonian(kx, ky) + eigenvalue, eigenvector = np.linalg.eig(H) + vector = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] # 价带波函数 + + 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 + + # vector = vector*cmath.exp(-1j*1) + # vector_delta_kx = vector_delta_kx*cmath.exp(-1j*1) + # vector_delta_ky = vector_delta_ky*cmath.exp(-1j*1) + # vector_delta_kx_ky = vector_delta_kx_ky*cmath.exp(-1j*(1+1e-8)) + + + rand = np.random.uniform(-pi, pi) + vector_delta_kx_ky = vector_delta_kx_ky*cmath.exp(-1j*rand) + + # 寻找近似的同一的规范 + phase_1_pre = 0 + phase_2_pre = pi + n_test = 10001 + for i0 in range(n_test): + test_1 = np.sum(np.abs(vector_delta_kx_ky*cmath.exp(1j*phase_1_pre) - vector)) + test_2 = np.sum(np.abs(vector_delta_kx_ky*cmath.exp(1j*phase_2_pre) - vector)) + if test_1 < 1e-6: + phase = phase_1_pre + print('Done with i0=', i0) + break + if i0 == n_test-1: + phase = phase_1_pre + print('Not Found with i0=', i0) + if test_1 < test_2: + if i0 == 0: + phase_1 = phase_1_pre-(phase_2_pre-phase_1_pre)/2 + phase_2 = phase_1_pre+(phase_2_pre-phase_1_pre)/2 + else: + phase_1 = phase_1_pre + phase_2 = phase_1_pre+(phase_2_pre-phase_1_pre)/2 + else: + if i0 == 0: + phase_1 = phase_2_pre-(phase_2_pre-phase_1_pre)/2 + phase_2 = phase_2_pre+(phase_2_pre-phase_1_pre)/2 + else: + phase_1 = phase_2_pre-(phase_2_pre-phase_1_pre)/2 + phase_2 = phase_2_pre + phase_1_pre = phase_1 + phase_2_pre = phase_2 + + vector_delta_kx_ky = vector_delta_kx_ky*cmath.exp(1j*phase) + print('随机的规范=', rand) # 可注释掉 + print('二分查找找到的规范=', phase) # 可注释掉 + print() # 可注释掉 + + + # 价带的波函数的贝里联络(berry connection) # 求导后内积 + A_x = np.dot(vector.transpose().conj(), (vector_delta_kx-vector)/delta) # 贝里联络Ax（x分量） + A_y = np.dot(vector.transpose().conj(), (vector_delta_ky-vector)/delta) # 贝里联络Ay（y分量） + + A_x_delta_ky = np.dot(vector_delta_ky.transpose().conj(), (vector_delta_kx_ky-vector_delta_ky)/delta) # 略偏离ky的贝里联络Ax + A_y_delta_kx = np.dot(vector_delta_kx.transpose().conj(), (vector_delta_kx_ky-vector_delta_kx)/delta) # 略偏离kx的贝里联络Ay + + # 贝里曲率(berry curvature) + F = (A_y_delta_kx-A_y)/delta-(A_x_delta_ky-A_x)/delta + + # 陈数(chern number) + chern_number = chern_number + F*(2*pi/n)**2 + chern_number = chern_number/(2*pi*1j) + print('Chern number = ', chern_number) + end_time = time.time() + print('运行时间(min)=', (end_time-start_time)/60) + + +if __name__ == '__main__': + main() diff --git a/academic_codes/2020.11.27_find_the_same_gauge_numerically_with_binary_search/find_the_same_gauge_numerically_with_guan.py b/academic_codes/2020.11.27_find_the_same_gauge_numerically_with_binary_search/find_the_same_gauge_numerically_with_guan.py new file mode 100644 index 0000000..bf8fe8b --- /dev/null +++ b/academic_codes/2020.11.27_find_the_same_gauge_numerically_with_binary_search/find_the_same_gauge_numerically_with_guan.py @@ -0,0 +1,78 @@ +""" +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/7516 +""" + +import numpy as np +from math import * +import cmath +import time +import guan + + +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))*(1+0j) + 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 = 100 # 积分密度 + delta = 1e-9 # 求导的偏离量 + chern_number = 0 # 陈数初始化 + for kx in np.arange(-pi, pi, 2*pi/n): + for ky in np.arange(-pi, pi, 2*pi/n): + H = hamiltonian(kx, ky) + eigenvalue, eigenvector = np.linalg.eig(H) + vector = eigenvector[:, np.argsort(np.real(eigenvalue))[0]] # 价带波函数 + + 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 + + # vector = vector*cmath.exp(-1j*1) + # vector_delta_kx = vector_delta_kx*cmath.exp(-1j*1) + # vector_delta_ky = vector_delta_ky*cmath.exp(-1j*1) + # vector_delta_kx_ky = vector_delta_kx_ky*cmath.exp(-1j*(1+1e-8)) + + rand = np.random.uniform(-pi, pi) + vector_delta_kx_ky = vector_delta_kx_ky*cmath.exp(-1j*rand) + + vector_delta_kx_ky = guan.find_vector_with_the_same_gauge_with_binary_search(vector_delta_kx_ky, vector) + + # 价带的波函数的贝里联络(berry connection) # 求导后内积 + A_x = np.dot(vector.transpose().conj(), (vector_delta_kx-vector)/delta) # 贝里联络Ax（x分量） + A_y = np.dot(vector.transpose().conj(), (vector_delta_ky-vector)/delta) # 贝里联络Ay（y分量） + + A_x_delta_ky = np.dot(vector_delta_ky.transpose().conj(), (vector_delta_kx_ky-vector_delta_ky)/delta) # 略偏离ky的贝里联络Ax + A_y_delta_kx = np.dot(vector_delta_kx.transpose().conj(), (vector_delta_kx_ky-vector_delta_kx)/delta) # 略偏离kx的贝里联络Ay + + # 贝里曲率(berry curvature) + F = (A_y_delta_kx-A_y)/delta-(A_x_delta_ky-A_x)/delta + + # 陈数(chern number) + chern_number = chern_number + F*(2*pi/n)**2 + chern_number = chern_number/(2*pi*1j) + print('Chern number = ', chern_number) + end_time = time.time() + print('运行时间(min)=', (end_time-start_time)/60) + + +if __name__ == '__main__': + main() \ No newline at end of file diff --git a/academic_codes/2021.03.01_Wilson_loop_in_SSH_model/Wilson_loop_in_SSH_model.py b/academic_codes/2021.03.01_Wilson_loop_in_SSH_model/Wilson_loop_in_SSH_model.py index d1c4135..5eec244 100755 --- a/academic_codes/2021.03.01_Wilson_loop_in_SSH_model/Wilson_loop_in_SSH_model.py +++ b/academic_codes/2021.03.01_Wilson_loop_in_SSH_model/Wilson_loop_in_SSH_model.py @@ -8,13 +8,12 @@ import cmath from math import * -def hamiltonian(k): +def hamiltonian(k): # SSH模型哈密顿量 gamma = 0.5 lambda0 = 1 - delta = 0 h = np.zeros((2, 2))*(1+0j) - h[0,0] = delta - h[1,1] = -delta + h[0,0] = 0 + h[1,1] = 0 h[0,1] = gamma+lambda0*cmath.exp(-1j*k) h[1,0] = gamma+lambda0*cmath.exp(1j*k) return h @@ -27,11 +26,16 @@ def main(): for k in k_array: vector = get_occupied_bands_vectors(k, hamiltonian) vector_array.append(vector) + # vector_array.append(vector*cmath.exp(1j*np.random.uniform(0, pi))) # 波函数固定一个规范 - index = np.argmax(np.abs(vector_array[0])) for i0 in range(Num_k): - vector_array[i0] = find_vector_with_fixed_gauge(vector_array[i0], index) + vector_array[i0] = find_vector_with_fixed_gauge_by_making_one_component_real(vector_array[i0]) + + # 波函数固定一个规范 + # import guan + # for i0 in range(Num_k): + # vector_array[i0] = guan.find_vector_with_fixed_gauge_by_making_one_component_real(vector_array[i0]) # 计算Wilson loop W_k = 1 @@ -51,9 +55,10 @@ def get_occupied_bands_vectors(x, matrix): return vector -def find_vector_with_fixed_gauge(vector, index): +def find_vector_with_fixed_gauge_by_making_one_component_real(vector, precision=0.005): + index = np.argmax(np.abs(vector)) sign_pre = np.sign(np.imag(vector[index])) - for phase in np.arange(0, 2*pi, 0.01): + for phase in np.arange(0, 2*pi, precision): sign = np.sign(np.imag(vector[index]*cmath.exp(1j*phase))) if np.abs(np.imag(vector[index]*cmath.exp(1j*phase))) < 1e-9 or sign == -sign_pre: break