diff --git a/API_Reference.py b/API_Reference.py index df48171..a7dc194 100644 --- a/API_Reference.py +++ b/API_Reference.py @@ -244,12 +244,18 @@ guan.print_or_write_scattering_matrix(fermi_energy, h00, h01, length=100, print_ # Module 9: topological invariant -chern_number = guan.calculate_chern_number_for_square_lattice(hamiltonian_function, precision=100, print_show=0) +chern_number = guan.calculate_chern_number_for_square_lattice_efficient_method(hamiltonian_function, precision=100, print_show=0) chern_number = guan.calculate_chern_number_for_square_lattice_with_wilson_loop(hamiltonian_function, precision_of_plaquettes=20, precision_of_wilson_loop=5, print_show=0) chern_number = guan.calculate_chern_number_for_square_lattice_with_wilson_loop_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], precision_of_plaquettes=20, precision_of_wilson_loop=5, print_show=0) +k_array, berry_curvature_array = guan.calculate_berry_curvature_with_efficient_method(hamiltonian_function, k_min=-math.pi, k_max=math.pi, precision=100, print_show=0) + +k_array, berry_curvature_array = guan.calculate_berry_curvature_with_wilson_loop(hamiltonian_function, k_min=-math.pi, k_max=math.pi, precision_of_plaquettes=20, precision_of_wilson_loop=5, print_show=0) + +k_array, berry_curvature_array = guan.calculate_berry_curvature_with_wilson_loop_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], k_min=-math.pi, k_max=math.pi, precision_of_plaquettes=20, precision_of_wilson_loop=5, print_show=0) + chern_number = guan.calculate_chern_number_for_honeycomb_lattice(hamiltonian_function, a=1, precision=300, print_show=0) wilson_loop_array = guan.calculate_wilson_loop(hamiltonian_function, k_min=-math.pi, k_max=math.pi, precision=100, print_show=0) diff --git a/PyPI/setup.cfg b/PyPI/setup.cfg index 7cae682..fb38f1d 100644 --- a/PyPI/setup.cfg +++ b/PyPI/setup.cfg @@ -1,7 +1,7 @@ [metadata] # replace with your username: name = guan -version = 0.0.122 +version = 0.0.123 author = guanjihuan author_email = guanjihuan@163.com description = An open source python package diff --git a/PyPI/src/guan.egg-info/PKG-INFO b/PyPI/src/guan.egg-info/PKG-INFO index bd3c597..47739e4 100644 --- a/PyPI/src/guan.egg-info/PKG-INFO +++ b/PyPI/src/guan.egg-info/PKG-INFO @@ -1,6 +1,6 @@ Metadata-Version: 2.1 Name: guan -Version: 0.0.122 +Version: 0.0.123 Summary: An open source python package Home-page: https://py.guanjihuan.com Author: guanjihuan diff --git a/PyPI/src/guan/__init__.py b/PyPI/src/guan/__init__.py index bd116e2..eb3b2be 100644 --- a/PyPI/src/guan/__init__.py +++ b/PyPI/src/guan/__init__.py @@ -2,7 +2,7 @@ # With this package, you can calculate band structures, density of states, quantum transport and topological invariant of tight-binding models by invoking the functions you need. Other frequently used functions are also integrated in this package, such as file reading/writing, figure plotting, data processing. -# The current version is guan-0.0.122, updated on August 13, 2022. +# The current version is guan-0.0.123, updated on August 13, 2022. # Installation: pip install --upgrade guan @@ -1518,7 +1518,7 @@ def print_or_write_scattering_matrix(fermi_energy, h00, h01, length=100, print_s # Module 9: topological invariant -def calculate_chern_number_for_square_lattice(hamiltonian_function, precision=100, print_show=0): +def calculate_chern_number_for_square_lattice_efficient_method(hamiltonian_function, precision=100, print_show=0): if np.array(hamiltonian_function(0, 0)).shape==(): dim = 1 else: @@ -1652,6 +1652,157 @@ def calculate_chern_number_for_square_lattice_with_wilson_loop_for_degenerate_ca chern_number = chern_number/(2*math.pi) return chern_number + +def calculate_berry_curvature_with_efficient_method(hamiltonian_function, k_min=-math.pi, k_max=math.pi, precision=100, print_show=0): + if np.array(hamiltonian_function(0, 0)).shape==(): + dim = 1 + else: + dim = np.array(hamiltonian_function(0, 0)).shape[0] + delta = (k_max-k_min)/precision + k_array = np.arange(k_min, k_max, delta) + berry_curvature_array = np.zeros((k_array.shape[0], k_array.shape[0], dim), dtype=complex) + i0 = 0 + for kx in k_array: + if print_show == 1: + print(kx) + j0 = 0 + for ky in k_array: + H = hamiltonian_function(kx, ky) + vector = guan.calculate_eigenvector(H) + H_delta_kx = hamiltonian_function(kx+delta, ky) + vector_delta_kx = guan.calculate_eigenvector(H_delta_kx) + H_delta_ky = hamiltonian_function(kx, ky+delta) + vector_delta_ky = guan.calculate_eigenvector(H_delta_ky) + H_delta_kx_ky = hamiltonian_function(kx+delta, ky+delta) + vector_delta_kx_ky = guan.calculate_eigenvector(H_delta_kx_ky) + for i in range(dim): + vector_i = vector[:, i] + vector_delta_kx_i = vector_delta_kx[:, i] + vector_delta_ky_i = vector_delta_ky[:, i] + vector_delta_kx_ky_i = vector_delta_kx_ky[:, i] + Ux = np.dot(np.conj(vector_i), vector_delta_kx_i)/abs(np.dot(np.conj(vector_i), vector_delta_kx_i)) + Uy = np.dot(np.conj(vector_i), vector_delta_ky_i)/abs(np.dot(np.conj(vector_i), vector_delta_ky_i)) + 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)) + 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)) + berry_curvature = cmath.log(Ux*Uy_x*(1/Ux_y)*(1/Uy))/delta/delta*1j + berry_curvature_array[j0, i0, i] = berry_curvature + j0 += 1 + i0 += 1 + return k_array, berry_curvature_array + +def calculate_berry_curvature_with_wilson_loop(hamiltonian_function, k_min=-math.pi, k_max=math.pi, precision_of_plaquettes=20, precision_of_wilson_loop=5, print_show=0): + if np.array(hamiltonian_function(0, 0)).shape==(): + dim = 1 + else: + dim = np.array(hamiltonian_function(0, 0)).shape[0] + delta = (k_max-k_min)/precision_of_plaquettes + k_array = np.arange(k_min, k_max, delta) + berry_curvature_array = np.zeros((k_array.shape[0], k_array.shape[0], dim), dtype=complex) + i00 = 0 + for kx in k_array: + if print_show == 1: + print(kx) + j00 = 0 + for ky in k_array: + vector_array = [] + # line_1 + for i0 in range(precision_of_wilson_loop): + H_delta = hamiltonian_function(kx+delta/precision_of_wilson_loop*i0, ky) + eigenvalue, eigenvector = np.linalg.eig(H_delta) + vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))] + vector_array.append(vector_delta) + # line_2 + for i0 in range(precision_of_wilson_loop): + H_delta = hamiltonian_function(kx+delta, ky+delta/precision_of_wilson_loop*i0) + eigenvalue, eigenvector = np.linalg.eig(H_delta) + vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))] + vector_array.append(vector_delta) + # line_3 + for i0 in range(precision_of_wilson_loop): + H_delta = hamiltonian_function(kx+delta-delta/precision_of_wilson_loop*i0, ky+delta) + eigenvalue, eigenvector = np.linalg.eig(H_delta) + vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))] + vector_array.append(vector_delta) + # line_4 + for i0 in range(precision_of_wilson_loop): + H_delta = hamiltonian_function(kx, ky+delta-delta/precision_of_wilson_loop*i0) + eigenvalue, eigenvector = np.linalg.eig(H_delta) + vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))] + 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]) + berry_curvature = np.log(np.diagonal(wilson_loop))/delta/delta*1j + berry_curvature_array[j00, i00, :]=berry_curvature + j00 += 1 + i00 += 1 + return k_array, berry_curvature_array + +def calculate_berry_curvature_with_wilson_loop_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], k_min=-math.pi, k_max=math.pi, precision_of_plaquettes=20, precision_of_wilson_loop=5, print_show=0): + delta = (k_max-k_min)/precision_of_plaquettes + k_array = np.arange(k_min, k_max, delta) + berry_curvature_array = np.zeros((k_array.shape[0], k_array.shape[0]), dtype=complex) + i000 = 0 + for kx in k_array: + if print_show == 1: + print(kx) + j000 = 0 + for ky in k_array: + vector_array = [] + # line_1 + for i0 in range(precision_of_wilson_loop): + H_delta = hamiltonian_function(kx+delta/precision_of_wilson_loop*i0, ky) + eigenvalue, eigenvector = np.linalg.eig(H_delta) + vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))] + vector_array.append(vector_delta) + # line_2 + for i0 in range(precision_of_wilson_loop): + H_delta = hamiltonian_function(kx+delta, ky+delta/precision_of_wilson_loop*i0) + eigenvalue, eigenvector = np.linalg.eig(H_delta) + vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))] + vector_array.append(vector_delta) + # line_3 + for i0 in range(precision_of_wilson_loop): + H_delta = hamiltonian_function(kx+delta-delta/precision_of_wilson_loop*i0, ky+delta) + eigenvalue, eigenvector = np.linalg.eig(H_delta) + vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))] + vector_array.append(vector_delta) + # line_4 + for i0 in range(precision_of_wilson_loop): + H_delta = hamiltonian_function(kx, ky+delta-delta/precision_of_wilson_loop*i0) + eigenvalue, eigenvector = np.linalg.eig(H_delta) + vector_delta = eigenvector[:, np.argsort(np.real(eigenvalue))] + vector_array.append(vector_delta) + wilson_loop = 1 + dim = len(index_of_bands) + for i0 in range(len(vector_array)-1): + dot_matrix = np.zeros((dim , dim), dtype=complex) + i01 = 0 + for dim1 in index_of_bands: + i02 = 0 + for dim2 in index_of_bands: + dot_matrix[i01, i02] = np.dot(vector_array[i0][:, dim1].transpose().conj(), vector_array[i0+1][:, dim2]) + i02 += 1 + i01 += 1 + det_value = np.linalg.det(dot_matrix) + wilson_loop = wilson_loop*det_value + dot_matrix_plus = np.zeros((dim , dim), dtype=complex) + i01 = 0 + for dim1 in index_of_bands: + i02 = 0 + for dim2 in index_of_bands: + dot_matrix_plus[i01, i02] = np.dot(vector_array[len(vector_array)-1][:, dim1].transpose().conj(), vector_array[0][:, dim2]) + i02 += 1 + i01 += 1 + det_value = np.linalg.det(dot_matrix_plus) + wilson_loop = wilson_loop*det_value + berry_curvature = np.log(wilson_loop)/delta/delta*1j + berry_curvature_array[j000, i000]=berry_curvature + j000 += 1 + i000 += 1 + return k_array, berry_curvature_array + def calculate_chern_number_for_honeycomb_lattice(hamiltonian_function, a=1, precision=300, print_show=0): if np.array(hamiltonian_function(0, 0)).shape==(): dim = 1 @@ -1715,9 +1866,6 @@ def calculate_wilson_loop(hamiltonian_function, k_min=-math.pi, k_max=math.pi, p - - - # Module 10: read and write def read_one_dimensional_data(filename='a', format='txt'):