From bc213ccc9d6bad02ca5f36480204b6cabe1e8758 Mon Sep 17 00:00:00 2001 From: guanjihuan Date: Tue, 3 Oct 2023 10:37:16 +0800 Subject: [PATCH] import only for the necessary need --- API_Reference/API_Reference.py | 8 + Source_Code/PyPI/src/guan/__init__.py | 313 +++++++++++++++++++++----- 2 files changed, 266 insertions(+), 55 deletions(-) diff --git a/API_Reference/API_Reference.py b/API_Reference/API_Reference.py index 7823061..9a81836 100644 --- a/API_Reference/API_Reference.py +++ b/API_Reference/API_Reference.py @@ -229,6 +229,7 @@ hamiltonian = guan.hamiltonian_of_cubic_lattice(k1, k2, k3) hamiltonian = guan.hamiltonian_of_ssh_model(k, v=0.6, w=1) # 石墨烯的哈密顿量 +import math hamiltonian = guan.hamiltonian_of_graphene(k1, k2, staggered_potential=0, t=1, a=1/math.sqrt(3)) # 石墨烯有效模型的哈密顿量 @@ -241,9 +242,11 @@ hamiltonian = guan.effective_hamiltonian_of_graphene_after_discretization(qx, qy hamiltonian = guan.hamiltonian_of_graphene_with_zigzag_in_quasi_one_dimension(k, N=10, M=0, t=1, period=0) # Haldane模型的哈密顿量 +import math hamiltonian = guan.hamiltonian_of_haldane_model(k1, k2, M=2/3, t1=1, t2=1/3, phi=math.pi/4, a=1/math.sqrt(3)) # 准一维Haldane模型条带的哈密顿量 +import math hamiltonian = guan.hamiltonian_of_haldane_model_in_quasi_one_dimension(k, N=10, M=2/3, t1=1, t2=1/3, phi=math.pi/4, period=0) # 一个量子反常霍尔效应的哈密顿量 @@ -580,21 +583,26 @@ chern_number = guan.calculate_chern_number_for_square_lattice_with_wilson_loop(h 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) # 通过高效法计算贝利曲率 +import math 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) # 通过高效法计算贝利曲率（可计算简并的情况） +import math k_array, berry_curvature_array = guan.calculate_berry_curvature_with_efficient_method_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], k_min=-math.pi, k_max=math.pi, precision=100, print_show=0) # 通过Wilson loop方法计算贝里曲率 +import math 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) # 通过Wilson loop方法计算贝里曲率（可计算简并的情况） +import math 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) # 计算蜂窝格子的陈数（高效法） chern_number = guan.calculate_chern_number_for_honeycomb_lattice(hamiltonian_function, a=1, precision=300, print_show=0) # 计算Wilson loop +import math 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/Source_Code/PyPI/src/guan/__init__.py b/Source_Code/PyPI/src/guan/__init__.py index 8520aeb..9a0ef42 100644 --- a/Source_Code/PyPI/src/guan/__init__.py +++ b/Source_Code/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-0.0.179, updated on September 29, 2023. +# The current version is guan-0.0.180, updated on December 03, 2023. # Installation: pip install --upgrade guan @@ -21,51 +21,6 @@ # # Module 11: read and write # # Module 12: data processing # # Module 13: file processing -# # Module 14: others - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -# import necessary packages - -import numpy as np -import math -import cmath -import guan - - - @@ -110,65 +65,101 @@ def test(): ## Pauli matrices def sigma_0(): + import numpy as np return np.eye(2) def sigma_x(): + import numpy as np return np.array([[0, 1],[1, 0]]) def sigma_y(): + import numpy as np return np.array([[0, -1j],[1j, 0]]) def sigma_z(): + import numpy as np return np.array([[1, 0],[0, -1]]) ## Kronecker product of Pauli matrices def sigma_00(): + import numpy as np + import guan return np.kron(guan.sigma_0(), guan.sigma_0()) def sigma_0x(): + import numpy as np + import guan return np.kron(guan.sigma_0(), guan.sigma_x()) def sigma_0y(): + import numpy as np + import guan return np.kron(guan.sigma_0(), guan.sigma_y()) def sigma_0z(): + import numpy as np + import guan return np.kron(guan.sigma_0(), guan.sigma_z()) def sigma_x0(): + import numpy as np + import guan return np.kron(guan.sigma_x(), guan.sigma_0()) def sigma_xx(): + import numpy as np + import guan return np.kron(guan.sigma_x(), guan.sigma_x()) def sigma_xy(): + import numpy as np + import guan return np.kron(guan.sigma_x(), guan.sigma_y()) def sigma_xz(): + import numpy as np + import guan return np.kron(guan.sigma_x(), guan.sigma_z()) def sigma_y0(): + import numpy as np + import guan return np.kron(guan.sigma_y(), guan.sigma_0()) def sigma_yx(): + import numpy as np + import guan return np.kron(guan.sigma_y(), guan.sigma_x()) def sigma_yy(): + import numpy as np + import guan return np.kron(guan.sigma_y(), guan.sigma_y()) def sigma_yz(): + import numpy as np + import guan return np.kron(guan.sigma_y(), guan.sigma_z()) def sigma_z0(): + import numpy as np + import guan return np.kron(guan.sigma_z(), guan.sigma_0()) def sigma_zx(): + import numpy as np + import guan return np.kron(guan.sigma_z(), guan.sigma_x()) def sigma_zy(): + import numpy as np + import guan return np.kron(guan.sigma_z(), guan.sigma_y()) def sigma_zz(): + import numpy as np + import guan return np.kron(guan.sigma_z(), guan.sigma_z()) @@ -208,6 +199,8 @@ def sigma_zz(): # 通过元胞和跃迁项得到一维的哈密顿量（需要输入k值） def one_dimensional_fourier_transform(k, unit_cell, hopping): + import numpy as np + import cmath unit_cell = np.array(unit_cell) hopping = np.array(hopping) hamiltonian = unit_cell+hopping*cmath.exp(1j*k)+hopping.transpose().conj()*cmath.exp(-1j*k) @@ -215,6 +208,8 @@ def one_dimensional_fourier_transform(k, unit_cell, hopping): # 通过元胞和跃迁项得到二维方格子的哈密顿量（需要输入k值） def two_dimensional_fourier_transform_for_square_lattice(k1, k2, unit_cell, hopping_1, hopping_2): + import numpy as np + import cmath unit_cell = np.array(unit_cell) hopping_1 = np.array(hopping_1) hopping_2 = np.array(hopping_2) @@ -223,6 +218,8 @@ def two_dimensional_fourier_transform_for_square_lattice(k1, k2, unit_cell, hopp # 通过元胞和跃迁项得到三维立方格子的哈密顿量（需要输入k值） def three_dimensional_fourier_transform_for_cubic_lattice(k1, k2, k3, unit_cell, hopping_1, hopping_2, hopping_3): + import numpy as np + import cmath unit_cell = np.array(unit_cell) hopping_1 = np.array(hopping_1) hopping_2 = np.array(hopping_2) @@ -233,28 +230,33 @@ def three_dimensional_fourier_transform_for_cubic_lattice(k1, k2, k3, unit_cell, # 通过元胞和跃迁项得到一维的哈密顿量（返回的哈密顿量为携带k的函数） def one_dimensional_fourier_transform_with_k(unit_cell, hopping): import functools + import guan hamiltonian_function = functools.partial(guan.one_dimensional_fourier_transform, unit_cell=unit_cell, hopping=hopping) return hamiltonian_function # 通过元胞和跃迁项得到二维方格子的哈密顿量（返回的哈密顿量为携带k的函数） def two_dimensional_fourier_transform_for_square_lattice_with_k1_k2(unit_cell, hopping_1, hopping_2): import functools + import guan hamiltonian_function = functools.partial(guan.two_dimensional_fourier_transform_for_square_lattice, unit_cell=unit_cell, hopping_1=hopping_1, hopping_2=hopping_2) return hamiltonian_function # 通过元胞和跃迁项得到三维立方格子的哈密顿量（返回的哈密顿量为携带k的函数） def three_dimensional_fourier_transform_for_cubic_lattice_with_k1_k2_k3(unit_cell, hopping_1, hopping_2, hopping_3): import functools + import guan hamiltonian_function = functools.partial(guan.three_dimensional_fourier_transform_for_cubic_lattice, unit_cell=unit_cell, hopping_1=hopping_1, hopping_2=hopping_2, hopping_3=hopping_3) return hamiltonian_function # 由实空间格矢得到倒空间格矢（一维） def calculate_one_dimensional_reciprocal_lattice_vector(a1): + import numpy as np b1 = 2*np.pi/a1 return b1 # 由实空间格矢得到倒空间格矢（二维） def calculate_two_dimensional_reciprocal_lattice_vectors(a1, a2): + import numpy as np a1 = np.array(a1) a2 = np.array(a2) a1 = np.append(a1, 0) @@ -268,6 +270,7 @@ def calculate_two_dimensional_reciprocal_lattice_vectors(a1, a2): # 由实空间格矢得到倒空间格矢（三维） def calculate_three_dimensional_reciprocal_lattice_vectors(a1, a2, a3): + import numpy as np a1 = np.array(a1) a2 = np.array(a2) a3 = np.array(a3) @@ -347,6 +350,7 @@ def calculate_three_dimensional_reciprocal_lattice_vectors_with_sympy(a1, a2, a3 # 构建一维的有限尺寸体系哈密顿量（可设置是否为周期边界条件） def hamiltonian_of_finite_size_system_along_one_direction(N, on_site=0, hopping=1, period=0): + import numpy as np on_site = np.array(on_site) hopping = np.array(hopping) if on_site.shape==(): @@ -366,6 +370,7 @@ def hamiltonian_of_finite_size_system_along_one_direction(N, on_site=0, hopping= # 构建二维的方格子有限尺寸体系哈密顿量（可设置是否为周期边界条件） def hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(N1, N2, on_site=0, hopping_1=1, hopping_2=1, period_1=0, period_2=0): + import numpy as np on_site = np.array(on_site) hopping_1 = np.array(hopping_1) hopping_2 = np.array(hopping_2) @@ -397,6 +402,7 @@ def hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(N1 # 构建三维的立方格子有限尺寸体系哈密顿量（可设置是否为周期边界条件） def hamiltonian_of_finite_size_system_along_three_directions_for_cubic_lattice(N1, N2, N3, on_site=0, hopping_1=1, hopping_2=1, hopping_3=1, period_1=0, period_2=0, period_3=0): + import numpy as np on_site = np.array(on_site) hopping_1 = np.array(hopping_1) hopping_2 = np.array(hopping_2) @@ -444,6 +450,7 @@ def hamiltonian_of_finite_size_system_along_three_directions_for_cubic_lattice(N # 构建有限尺寸的SSH模型哈密顿量 def hamiltonian_of_finite_size_ssh_model(N, v=0.6, w=1, onsite_1=0, onsite_2=0, period=1): + import numpy as np hamiltonian = np.zeros((2*N, 2*N)) for i in range(N): hamiltonian[i*2+0, i*2+0] = onsite_1 @@ -460,6 +467,7 @@ def hamiltonian_of_finite_size_ssh_model(N, v=0.6, w=1, onsite_1=0, onsite_2=0, # 获取Zigzag边的石墨烯条带的元胞间跃迁 def get_hopping_term_of_graphene_ribbon_along_zigzag_direction(N, eta=0): + import numpy as np hopping = np.zeros((4*N, 4*N), dtype=complex) for i0 in range(N): hopping[4*i0+0, 4*i0+0] = eta @@ -472,6 +480,8 @@ def get_hopping_term_of_graphene_ribbon_along_zigzag_direction(N, eta=0): # 构建有限尺寸的石墨烯哈密顿量（可设置是否为周期边界条件） def hamiltonian_of_finite_size_system_along_two_directions_for_graphene(N1, N2, period_1=0, period_2=0): + import numpy as np + import guan on_site = guan.hamiltonian_of_finite_size_system_along_one_direction(4) hopping_1 = guan.get_hopping_term_of_graphene_ribbon_along_zigzag_direction(1) hopping_2 = np.zeros((4, 4), dtype=complex) @@ -481,6 +491,7 @@ def hamiltonian_of_finite_size_system_along_two_directions_for_graphene(N1, N2, # 获取石墨烯有效模型沿着x方向的在位能和跃迁项（其中，动量qy为参数） def get_onsite_and_hopping_terms_of_2d_effective_graphene_along_one_direction(qy, t=1, staggered_potential=0, eta=0, valley_index=0): + import numpy as np constant = -np.sqrt(3)/2 h00 = np.zeros((2, 2), dtype=complex) h00[0, 0] = staggered_potential @@ -500,6 +511,7 @@ def get_onsite_and_hopping_terms_of_2d_effective_graphene_along_one_direction(qy # 获取BHZ模型的在位能和跃迁项 def get_onsite_and_hopping_terms_of_bhz_model(A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, M=-0.01, a=1): + import numpy as np E_s = C+M-4*(D+B)/(a**2) E_p = C-M-4*(D-B)/(a**2) V_ss = (D+B)/(a**2) @@ -532,6 +544,7 @@ def get_onsite_and_hopping_terms_of_bhz_model(A=0.3645/5, B=-0.686/25, C=0, D=-0 # 获取半个BHZ模型的在位能和跃迁项（自旋向上） def get_onsite_and_hopping_terms_of_half_bhz_model_for_spin_up(A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, M=-0.01, a=1): + import numpy as np E_s = C+M-4*(D+B)/(a**2) E_p = C-M-4*(D-B)/(a**2) V_ss = (D+B)/(a**2) @@ -554,6 +567,7 @@ def get_onsite_and_hopping_terms_of_half_bhz_model_for_spin_up(A=0.3645/5, B=-0. # 获取半个BHZ模型的在位能和跃迁项（自旋向下） def get_onsite_and_hopping_terms_of_half_bhz_model_for_spin_down(A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, M=-0.01, a=1): + import numpy as np E_s = C+M-4*(D+B)/(a**2) E_p = C-M-4*(D-B)/(a**2) V_ss = (D+B)/(a**2) @@ -625,16 +639,20 @@ def get_onsite_and_hopping_terms_of_half_bhz_model_for_spin_down(A=0.3645/5, B=- # 一维链的哈密顿量 def hamiltonian_of_simple_chain(k): + import guan hamiltonian = guan.one_dimensional_fourier_transform(k, unit_cell=0, hopping=1) return hamiltonian # 二维方格子的哈密顿量 def hamiltonian_of_square_lattice(k1, k2): + import guan hamiltonian = guan.two_dimensional_fourier_transform_for_square_lattice(k1, k2, unit_cell=0, hopping_1=1, hopping_2=1) return hamiltonian # 准一维方格子条带的哈密顿量 def hamiltonian_of_square_lattice_in_quasi_one_dimension(k, N=10, period=0): + import numpy as np + import guan h00 = np.zeros((N, N), dtype=complex) # hopping in a unit cell h01 = np.zeros((N, N), dtype=complex) # hopping between unit cells for i in range(N-1): @@ -650,18 +668,25 @@ def hamiltonian_of_square_lattice_in_quasi_one_dimension(k, N=10, period=0): # 三维立方格子的哈密顿量 def hamiltonian_of_cubic_lattice(k1, k2, k3): + import guan hamiltonian = guan.three_dimensional_fourier_transform_for_cubic_lattice(k1, k2, k3, unit_cell=0, hopping_1=1, hopping_2=1, hopping_3=1) return hamiltonian # SSH模型的哈密顿量 def hamiltonian_of_ssh_model(k, v=0.6, w=1): + import numpy as np + import cmath hamiltonian = np.zeros((2, 2), dtype=complex) hamiltonian[0,1] = v+w*cmath.exp(-1j*k) hamiltonian[1,0] = v+w*cmath.exp(1j*k) return hamiltonian # 石墨烯的哈密顿量 +import math def hamiltonian_of_graphene(k1, k2, staggered_potential=0, t=1, a=1/math.sqrt(3)): + import numpy as np + import cmath + import math h0 = np.zeros((2, 2), dtype=complex) # mass term h1 = np.zeros((2, 2), dtype=complex) # nearest hopping h0[0, 0] = staggered_potential @@ -673,6 +698,7 @@ def hamiltonian_of_graphene(k1, k2, staggered_potential=0, t=1, a=1/math.sqrt(3) # 石墨烯有效模型的哈密顿量 def effective_hamiltonian_of_graphene(qx, qy, t=1, staggered_potential=0, valley_index=0): + import numpy as np hamiltonian = np.zeros((2, 2), dtype=complex) hamiltonian[0, 0] = staggered_potential hamiltonian[1, 1] = -staggered_potential @@ -687,6 +713,7 @@ def effective_hamiltonian_of_graphene(qx, qy, t=1, staggered_potential=0, valley # 石墨烯有效模型离散化后的哈密顿量 def effective_hamiltonian_of_graphene_after_discretization(qx, qy, t=1, staggered_potential=0, valley_index=0): + import numpy as np hamiltonian = np.zeros((2, 2), dtype=complex) hamiltonian[0, 0] = staggered_potential hamiltonian[1, 1] = -staggered_potential @@ -701,6 +728,8 @@ def effective_hamiltonian_of_graphene_after_discretization(qx, qy, t=1, staggere # 准一维Zigzag边石墨烯条带的哈密顿量 def hamiltonian_of_graphene_with_zigzag_in_quasi_one_dimension(k, N=10, M=0, t=1, period=0): + import numpy as np + import guan h00 = np.zeros((4*N, 4*N), dtype=complex) # hopping in a unit cell h01 = np.zeros((4*N, 4*N), dtype=complex) # hopping between unit cells for i in range(N): @@ -727,7 +756,11 @@ def hamiltonian_of_graphene_with_zigzag_in_quasi_one_dimension(k, N=10, M=0, t=1 return hamiltonian # Haldane模型的哈密顿量 +import math def hamiltonian_of_haldane_model(k1, k2, M=2/3, t1=1, t2=1/3, phi=math.pi/4, a=1/math.sqrt(3)): + import numpy as np + import cmath + import math h0 = np.zeros((2, 2), dtype=complex) # mass term h1 = np.zeros((2, 2), dtype=complex) # nearest hopping h2 = np.zeros((2, 2), dtype=complex) # next nearest hopping @@ -741,7 +774,10 @@ def hamiltonian_of_haldane_model(k1, k2, M=2/3, t1=1, t2=1/3, phi=math.pi/4, a=1 return hamiltonian # 准一维Haldane模型条带的哈密顿量 +import math def hamiltonian_of_haldane_model_in_quasi_one_dimension(k, N=10, M=2/3, t1=1, t2=1/3, phi=math.pi/4, period=0): + import numpy as np + import cmath h00 = np.zeros((4*N, 4*N), dtype=complex) # hopping in a unit cell h01 = np.zeros((4*N, 4*N), dtype=complex) # hopping between unit cells for i in range(N): @@ -791,6 +827,8 @@ def hamiltonian_of_haldane_model_in_quasi_one_dimension(k, N=10, M=2/3, t1=1, t2 # 一个量子反常霍尔效应的哈密顿量 def hamiltonian_of_one_QAH_model(k1, k2, t1=1, t2=1, t3=0.5, m=-1): + import numpy as np + import math hamiltonian = np.zeros((2, 2), dtype=complex) hamiltonian[0, 1] = 2*t1*math.cos(k1)-1j*2*t1*math.cos(k2) hamiltonian[1, 0] = 2*t1*math.cos(k1)+1j*2*t1*math.cos(k2) @@ -800,6 +838,8 @@ def hamiltonian_of_one_QAH_model(k1, k2, t1=1, t2=1, t3=0.5, m=-1): # BHZ模型的哈密顿量 def hamiltonian_of_bhz_model(kx, ky, A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, M=-0.01): + import numpy as np + import math hamiltonian = np.zeros((4, 4), dtype=complex) varepsilon = C-2*D*(2-math.cos(kx)-math.cos(ky)) d3 = -2*B*(2-(M/2/B)-math.cos(kx)-math.cos(ky)) @@ -816,6 +856,8 @@ def hamiltonian_of_bhz_model(kx, ky, A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, # 半BHZ模型的哈密顿量（自旋向上） def hamiltonian_of_half_bhz_model_for_spin_up(kx, ky, A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, M=-0.01): + import numpy as np + import math hamiltonian = np.zeros((2, 2), dtype=complex) varepsilon = C-2*D*(2-math.cos(kx)-math.cos(ky)) d3 = -2*B*(2-(M/2/B)-math.cos(kx)-math.cos(ky)) @@ -828,6 +870,8 @@ def hamiltonian_of_half_bhz_model_for_spin_up(kx, ky, A=0.3645/5, B=-0.686/25, C # 半BHZ模型的哈密顿量（自旋向下） def hamiltonian_of_half_bhz_model_for_spin_down(kx, ky, A=0.3645/5, B=-0.686/25, C=0, D=-0.512/25, M=-0.01): + import numpy as np + import math hamiltonian = np.zeros((2, 2), dtype=complex) varepsilon = C-2*D*(2-math.cos(kx)-math.cos(ky)) d3 = -2*B*(2-(M/2/B)-math.cos(kx)-math.cos(ky)) @@ -840,6 +884,8 @@ def hamiltonian_of_half_bhz_model_for_spin_down(kx, ky, A=0.3645/5, B=-0.686/25, # BBH模型的哈密顿量 def hamiltonian_of_bbh_model(kx, ky, gamma_x=0.5, gamma_y=0.5, lambda_x=1, lambda_y=1): + import numpy as np + import cmath # label of atoms in a unit cell # (2) —— (0) # | | @@ -857,6 +903,8 @@ def hamiltonian_of_bbh_model(kx, ky, gamma_x=0.5, gamma_y=0.5, lambda_x=1, lambd # Kagome模型的哈密顿量 def hamiltonian_of_kagome_lattice(kx, ky, t=1): + import numpy as np + import math k1_dot_a1 = kx k2_dot_a2 = kx/2+ky*math.sqrt(3)/2 k3_dot_a3 = -kx/2+ky*math.sqrt(3)/2 @@ -920,6 +968,7 @@ def hamiltonian_of_kagome_lattice(kx, ky, t=1): # 计算哈密顿量的本征值 def calculate_eigenvalue(hamiltonian): + import numpy as np if np.array(hamiltonian).shape==(): eigenvalue = np.real(hamiltonian) else: @@ -928,6 +977,7 @@ def calculate_eigenvalue(hamiltonian): # 输入哈密顿量函数（带一组参数），计算一组参数下的本征值，返回本征值向量组 def calculate_eigenvalue_with_one_parameter(x_array, hamiltonian_function, print_show=0): + import numpy as np dim_x = np.array(x_array).shape[0] i0 = 0 if np.array(hamiltonian_function(0)).shape==(): @@ -950,6 +1000,7 @@ def calculate_eigenvalue_with_one_parameter(x_array, hamiltonian_function, print # 输入哈密顿量函数（带两组参数），计算两组参数下的本征值，返回本征值向量组 def calculate_eigenvalue_with_two_parameters(x_array, y_array, hamiltonian_function, print_show=0, print_show_more=0): + import numpy as np dim_x = np.array(x_array).shape[0] dim_y = np.array(y_array).shape[0] if np.array(hamiltonian_function(0,0)).shape==(): @@ -982,11 +1033,14 @@ def calculate_eigenvalue_with_two_parameters(x_array, y_array, hamiltonian_funct # 计算哈密顿量的本征矢 def calculate_eigenvector(hamiltonian): + import numpy as np eigenvalue, eigenvector = np.linalg.eigh(hamiltonian) return eigenvector # 通过二分查找的方法获取和相邻波函数一样规范的波函数 def find_vector_with_the_same_gauge_with_binary_search(vector_target, vector_ref, show_error=1, show_times=0, show_phase=0, n_test=1000, precision=1e-6): + import numpy as np + import cmath phase_1_pre = 0 phase_2_pre = np.pi for i0 in range(n_test): @@ -1024,6 +1078,8 @@ def find_vector_with_the_same_gauge_with_binary_search(vector_target, vector_ref # 通过使得波函数的一个非零分量为实数，得到固定规范的波函数 def find_vector_with_fixed_gauge_by_making_one_component_real(vector, precision=0.005, index=None): + import numpy as np + import cmath vector = np.array(vector) if index == None: index = np.argmax(np.abs(vector)) @@ -1036,10 +1092,12 @@ def find_vector_with_fixed_gauge_by_making_one_component_real(vector, precision= vector = vector*cmath.exp(1j*phase) if np.real(vector[index]) < 0: vector = -vector - return vector + return vector # 通过使得波函数的一个非零分量为实数，得到固定规范的波函数（在一组波函数中选取最大的那个分量） def find_vector_array_with_fixed_gauge_by_making_one_component_real(vector_array, precision=0.005): + import numpy as np + import guan vector_sum = 0 Num_k = np.array(vector_array).shape[0] for i0 in range(Num_k): @@ -1051,6 +1109,9 @@ def find_vector_array_with_fixed_gauge_by_making_one_component_real(vector_array # 旋转两个简并的波函数（说明：参数比较多，效率不高） def rotation_of_degenerate_vectors(vector1, vector2, index1=None, index2=None, precision=0.01, criterion=0.01, show_theta=0): + import numpy as np + import math + import cmath vector1 = np.array(vector1) vector2 = np.array(vector2) if index1 == None: @@ -1077,6 +1138,8 @@ def rotation_of_degenerate_vectors(vector1, vector2, index1=None, index2=None, p # 旋转两个简并的波函数向量组（说明：参数比较多，效率不高） def rotation_of_degenerate_vectors_array(vector1_array, vector2_array, precision=0.01, criterion=0.01, show_theta=0): + import numpy as np + import guan Num_k = np.array(vector1_array).shape[0] vector1_sum = 0 for i0 in range(Num_k): @@ -1136,6 +1199,7 @@ def rotation_of_degenerate_vectors_array(vector1_array, vector2_array, precision # 输入哈密顿量，得到格林函数 def green_function(fermi_energy, hamiltonian, broadening, self_energy=0): + import numpy as np if np.array(hamiltonian).shape==(): dim = 1 else: @@ -1145,6 +1209,7 @@ def green_function(fermi_energy, hamiltonian, broadening, self_energy=0): # 在Dyson方程中的一个中间格林函数G_{nn}^{n} def green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening, self_energy=0): + import numpy as np h01 = np.array(h01) if np.array(h00).shape==(): dim = 1 @@ -1155,22 +1220,26 @@ def green_function_nn_n(fermi_energy, h00, h01, green_nn_n_minus, broadening, se # 在Dyson方程中的一个中间格林函数G_{in}^{n} def green_function_in_n(green_in_n_minus, h01, green_nn_n): + import numpy as np green_in_n = np.dot(np.dot(green_in_n_minus, h01), green_nn_n) return green_in_n # 在Dyson方程中的一个中间格林函数G_{ni}^{n} def green_function_ni_n(green_nn_n, h01, green_ni_n_minus): + import numpy as np h01 = np.array(h01) green_ni_n = np.dot(np.dot(green_nn_n, h01.transpose().conj()), green_ni_n_minus) return green_ni_n # 在Dyson方程中的一个中间格林函数G_{ii}^{n} def green_function_ii_n(green_ii_n_minus, green_in_n_minus, h01, green_nn_n, green_ni_n_minus): + import numpy as np green_ii_n = green_ii_n_minus+np.dot(np.dot(np.dot(np.dot(green_in_n_minus, h01), green_nn_n), h01.transpose().conj()),green_ni_n_minus) return green_ii_n # 计算转移矩阵（该矩阵可以用来计算表面格林函数） def transfer_matrix(fermi_energy, h00, h01): + import numpy as np h01 = np.array(h01) if np.array(h00).shape==(): dim = 1 @@ -1185,6 +1254,7 @@ def transfer_matrix(fermi_energy, h00, h01): # 计算电极的表面格林函数 def surface_green_function_of_lead(fermi_energy, h00, h01): + import numpy as np h01 = np.array(h01) if np.array(h00).shape==(): dim = 1 @@ -1209,6 +1279,8 @@ def surface_green_function_of_lead(fermi_energy, h00, h01): # 计算电极的自能（基于Dyson方程的小矩阵形式） def self_energy_of_lead(fermi_energy, h00, h01): + import numpy as np + import guan h01 = np.array(h01) right_lead_surface, left_lead_surface = guan.surface_green_function_of_lead(fermi_energy, h00, h01) right_self_energy = np.dot(np.dot(h01, right_lead_surface), h01.transpose().conj()) @@ -1219,6 +1291,8 @@ def self_energy_of_lead(fermi_energy, h00, h01): # 计算电极的自能（基于中心区整体的大矩阵形式） def self_energy_of_lead_with_h_LC_and_h_CR(fermi_energy, h00, h01, h_LC, h_CR): + import numpy as np + import guan h_LC = np.array(h_LC) h_CR = np.array(h_CR) right_lead_surface, left_lead_surface = guan.surface_green_function_of_lead(fermi_energy, h00, h01) @@ -1230,6 +1304,8 @@ def self_energy_of_lead_with_h_LC_and_h_CR(fermi_energy, h00, h01, h_LC, h_CR): # 计算电极的自能（基于中心区整体的大矩阵形式，可适用于多端电导的计算） def self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00, h01, h_lead_to_center): + import numpy as np + import guan h_lead_to_center = np.array(h_lead_to_center) right_lead_surface, left_lead_surface = guan.surface_green_function_of_lead(fermi_energy, h00, h01) self_energy = np.dot(np.dot(h_lead_to_center.transpose().conj(), right_lead_surface), h_lead_to_center) @@ -1238,6 +1314,8 @@ def self_energy_of_lead_with_h_lead_to_center(fermi_energy, h00, h01, h_lead_to_ # 计算考虑电极自能后的中心区的格林函数 def green_function_with_leads(fermi_energy, h00, h01, h_LC, h_CR, center_hamiltonian): + import numpy as np + import guan dim = np.array(center_hamiltonian).shape[0] right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead_with_h_LC_and_h_CR(fermi_energy, h00, h01, h_LC, h_CR) green = np.linalg.inv(fermi_energy*np.identity(dim)-center_hamiltonian-left_self_energy-right_self_energy) @@ -1245,6 +1323,8 @@ def green_function_with_leads(fermi_energy, h00, h01, h_LC, h_CR, center_hamilto # 计算用于计算局域电流的格林函数G_n def electron_correlation_function_green_n_for_local_current(fermi_energy, h00, h01, h_LC, h_CR, center_hamiltonian): + import numpy as np + import guan right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead_with_h_LC_and_h_CR(fermi_energy, h00, h01, h_LC, h_CR) green = guan.green_function(fermi_energy, center_hamiltonian, broadening=0, self_energy=left_self_energy+right_self_energy) G_n = np.imag(np.dot(np.dot(green, gamma_left), green.transpose().conj())) @@ -1288,24 +1368,32 @@ def electron_correlation_function_green_n_for_local_current(fermi_energy, h00, h # 计算体系的总态密度 def total_density_of_states(fermi_energy, hamiltonian, broadening=0.01): + import numpy as np + import math + import guan green = guan.green_function(fermi_energy, hamiltonian, broadening) total_dos = -np.trace(np.imag(green))/math.pi return total_dos # 对于不同费米能，计算体系的总态密度 def total_density_of_states_with_fermi_energy_array(fermi_energy_array, hamiltonian, broadening=0.01, print_show=0): + import numpy as np + import guan dim = np.array(fermi_energy_array).shape[0] total_dos_array = np.zeros(dim) i0 = 0 for fermi_energy in fermi_energy_array: if print_show == 1: print(fermi_energy) - total_dos_array[i0] = total_density_of_states(fermi_energy, hamiltonian, broadening) + total_dos_array[i0] = guan.total_density_of_states(fermi_energy, hamiltonian, broadening) i0 += 1 return total_dos_array # 计算方格子的局域态密度（其中，哈密顿量的维度为：dim_hamiltonian = N1*N2*internal_degree） def local_density_of_states_for_square_lattice(fermi_energy, hamiltonian, N1, N2, internal_degree=1, broadening=0.01): + import numpy as np + import math + import guan green = guan.green_function(fermi_energy, hamiltonian, broadening) local_dos = np.zeros((N2, N1)) for i1 in range(N1): @@ -1316,6 +1404,9 @@ def local_density_of_states_for_square_lattice(fermi_energy, hamiltonian, N1, N2 # 计算立方格子的局域态密度（其中，哈密顿量的维度为：dim_hamiltonian = N1*N2*N3*internal_degree） def local_density_of_states_for_cubic_lattice(fermi_energy, hamiltonian, N1, N2, N3, internal_degree=1, broadening=0.01): + import numpy as np + import math + import guan green = guan.green_function(fermi_energy, hamiltonian, broadening) local_dos = np.zeros((N3, N2, N1)) for i1 in range(N1): @@ -1327,6 +1418,9 @@ def local_density_of_states_for_cubic_lattice(fermi_energy, hamiltonian, N1, N2, # 利用Dyson方程，计算方格子的局域态密度（其中，h00的维度为：dim_h00 = N2*internal_degree） def local_density_of_states_for_square_lattice_using_dyson_equation(fermi_energy, h00, h01, N2, N1, internal_degree=1, broadening=0.01): + import numpy as np + import math + import guan local_dos = np.zeros((N2, N1)) green_11_1 = guan.green_function(fermi_energy, h00, broadening) for i1 in range(N1): @@ -1357,6 +1451,9 @@ def local_density_of_states_for_square_lattice_using_dyson_equation(fermi_energy # 利用Dyson方程，计算立方格子的局域态密度（其中，h00的维度为：dim_h00 = N2*N3*internal_degree） def local_density_of_states_for_cubic_lattice_using_dyson_equation(fermi_energy, h00, h01, N3, N2, N1, internal_degree=1, broadening=0.01): + import numpy as np + import math + import guan local_dos = np.zeros((N3, N2, N1)) green_11_1 = guan.green_function(fermi_energy, h00, broadening) for i1 in range(N1): @@ -1388,6 +1485,9 @@ def local_density_of_states_for_cubic_lattice_using_dyson_equation(fermi_energy, # 利用Dyson方程，计算方格子条带（考虑了电极自能）的局域态密度（其中，h00的维度为：dim_h00 = N2*internal_degree） def local_density_of_states_for_square_lattice_with_self_energy_using_dyson_equation(fermi_energy, h00, h01, N2, N1, right_self_energy, left_self_energy, internal_degree=1, broadening=0.01): + import numpy as np + import math + import guan local_dos = np.zeros((N2, N1)) green_11_1 = guan.green_function(fermi_energy, h00+left_self_energy, broadening) for i1 in range(N1): @@ -1472,7 +1572,9 @@ def local_density_of_states_for_square_lattice_with_self_energy_using_dyson_equa # 计算电导 def calculate_conductance(fermi_energy, h00, h01, length=100): + import numpy as np import copy + import guan right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01) for ix in range(length): if ix == 0: @@ -1489,6 +1591,8 @@ def calculate_conductance(fermi_energy, h00, h01, length=100): # 计算不同费米能下的电导 def calculate_conductance_with_fermi_energy_array(fermi_energy_array, h00, h01, length=100, print_show=0): + import numpy as np + import guan dim = np.array(fermi_energy_array).shape[0] conductance_array = np.zeros(dim) i0 = 0 @@ -1501,7 +1605,9 @@ def calculate_conductance_with_fermi_energy_array(fermi_energy_array, h00, h01, # 计算在势垒散射下的电导 def calculate_conductance_with_barrier(fermi_energy, h00, h01, length=100, barrier_length=20, barrier_potential=1): + import numpy as np import copy + import guan right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01) dim = np.array(h00).shape[0] for ix in range(length): @@ -1522,7 +1628,9 @@ def calculate_conductance_with_barrier(fermi_energy, h00, h01, length=100, barri # 计算在无序散射下的电导 def calculate_conductance_with_disorder(fermi_energy, h00, h01, disorder_intensity=2.0, disorder_concentration=1.0, length=100, calculation_times=1): + import numpy as np import copy + import guan right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01) dim = np.array(h00).shape[0] conductance_averaged = 0 @@ -1548,7 +1656,9 @@ def calculate_conductance_with_disorder(fermi_energy, h00, h01, disorder_intensi # 计算在无序垂直切片的散射下的电导 def calculate_conductance_with_slice_disorder(fermi_energy, h00, h01, disorder_intensity=2.0, disorder_concentration=1.0, length=100): + import numpy as np import copy + import guan right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01) dim = np.array(h00).shape[0] for ix in range(length+2): @@ -1569,7 +1679,9 @@ def calculate_conductance_with_slice_disorder(fermi_energy, h00, h01, disorder_i # 计算在无序水平切片的散射下的电导 def calculate_conductance_with_disorder_inside_unit_cell_which_keeps_translational_symmetry(fermi_energy, h00, h01, disorder_intensity=2.0, disorder_concentration=1.0, length=100): + import numpy as np import copy + import guan right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01) dim = np.array(h00).shape[0] disorder = np.zeros((dim, dim)) @@ -1591,7 +1703,9 @@ def calculate_conductance_with_disorder_inside_unit_cell_which_keeps_translation # 计算在随机空位的散射下的电导 def calculate_conductance_with_random_vacancy(fermi_energy, h00, h01, vacancy_concentration=0.5, vacancy_potential=1e9, length=100): + import numpy as np import copy + import guan right_self_energy, left_self_energy, gamma_right, gamma_left = guan.self_energy_of_lead(fermi_energy, h00, h01) dim = np.array(h00).shape[0] for ix in range(length+2): @@ -1613,6 +1727,8 @@ def calculate_conductance_with_random_vacancy(fermi_energy, h00, h01, vacancy_co # 计算在不同无序散射强度下的电导 def calculate_conductance_with_disorder_intensity_array(fermi_energy, h00, h01, disorder_intensity_array, disorder_concentration=1.0, length=100, calculation_times=1, print_show=0): + import numpy as np + import guan dim = np.array(disorder_intensity_array).shape[0] conductance_array = np.zeros(dim) i0 = 0 @@ -1627,6 +1743,8 @@ def calculate_conductance_with_disorder_intensity_array(fermi_energy, h00, h01, # 计算在不同无序浓度下的电导 def calculate_conductance_with_disorder_concentration_array(fermi_energy, h00, h01, disorder_concentration_array, disorder_intensity=2.0, length=100, calculation_times=1, print_show=0): + import numpy as np + import guan dim = np.array(disorder_concentration_array).shape[0] conductance_array = np.zeros(dim) i0 = 0 @@ -1641,6 +1759,8 @@ def calculate_conductance_with_disorder_concentration_array(fermi_energy, h00, h # 计算在不同无序散射长度下的电导 def calculate_conductance_with_scattering_length_array(fermi_energy, h00, h01, length_array, disorder_intensity=2.0, disorder_concentration=1.0, calculation_times=1, print_show=0): + import numpy as np + import guan dim = np.array(length_array).shape[0] conductance_array = np.zeros(dim) i0 = 0 @@ -1657,6 +1777,8 @@ def calculate_conductance_with_scattering_length_array(fermi_energy, h00, h01, l # 计算得到Gamma矩阵和格林函数，用于计算六端口的量子输运 def get_gamma_array_and_green_for_six_terminal_transmission(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width=10, length=50, internal_degree=1, moving_step_of_leads=10): + import numpy as np + import guan # ---------------- Geometry ---------------- # lead2 lead3 # lead1(L) lead4(R) @@ -1701,6 +1823,8 @@ def get_gamma_array_and_green_for_six_terminal_transmission(fermi_energy, h00_fo # 计算六端口的透射矩阵 def calculate_six_terminal_transmission_matrix(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width=10, length=50, internal_degree=1, moving_step_of_leads=10): + import numpy as np + import guan gamma_array, green = guan.get_gamma_array_and_green_for_six_terminal_transmission(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width, length, internal_degree, moving_step_of_leads) transmission_matrix = np.zeros((6, 6), dtype=complex) channel_lead_4 = guan.calculate_conductance(fermi_energy, h00_for_lead_4, h01_for_lead_4, length=3) @@ -1723,6 +1847,8 @@ def calculate_six_terminal_transmission_matrix(fermi_energy, h00_for_lead_4, h01 # 计算从电极1出发的透射系数 def calculate_six_terminal_transmissions_from_lead_1(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width=10, length=50, internal_degree=1, moving_step_of_leads=10): + import numpy as np + import guan gamma_array, green = guan.get_gamma_array_and_green_for_six_terminal_transmission(fermi_energy, h00_for_lead_4, h01_for_lead_4, h00_for_lead_2, h01_for_lead_2, center_hamiltonian, width, length, internal_degree, moving_step_of_leads) transmission_12 = np.real(np.trace(np.dot(np.dot(np.dot(gamma_array[0], green), gamma_array[1]), green.transpose().conj()))) transmission_13 = np.real(np.trace(np.dot(np.dot(np.dot(gamma_array[0], green), gamma_array[2]), green.transpose().conj()))) @@ -1735,6 +1861,7 @@ def calculate_six_terminal_transmissions_from_lead_1(fermi_energy, h00_for_lead_ # 通过动量k的虚部，判断通道为传播通道还是衰减通道 def if_active_channel(k_of_channel): + import numpy as np if np.abs(np.imag(k_of_channel))<1e-6: if_active = 1 else: @@ -1743,7 +1870,10 @@ def if_active_channel(k_of_channel): # 获取通道的动量和速度，用于计算散射矩阵 def get_k_and_velocity_of_channel(fermi_energy, h00, h01): + import numpy as np + import math import copy + import guan if np.array(h00).shape==(): dim = 1 else: @@ -1776,6 +1906,8 @@ def get_k_and_velocity_of_channel(fermi_energy, h00, h01): # 获取分类后的动量和速度，以及U和F，用于计算散射矩阵 def get_classified_k_velocity_u_and_f(fermi_energy, h00, h01): + import numpy as np + import guan if np.array(h00).shape==(): dim = 1 else: @@ -1826,7 +1958,10 @@ def get_classified_k_velocity_u_and_f(fermi_energy, h00, h01): # 计算散射矩阵 def calculate_scattering_matrix(fermi_energy, h00, h01, length=100): + import numpy as np + import math import copy + import guan h01 = np.array(h01) if np.array(h00).shape==(): dim = 1 @@ -1868,6 +2003,7 @@ def calculate_scattering_matrix(fermi_energy, h00, h01, length=100): # 从散射矩阵中，获取散射矩阵的信息 def information_of_scattering_matrix(transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active): + import numpy as np if np.array(transmission_matrix).shape==(): dim = 1 else: @@ -1888,6 +2024,7 @@ def information_of_scattering_matrix(transmission_matrix, reflection_matrix, k_r # 已知h00和h01，计算散射矩阵并获得散射矩阵的信息 def calculate_scattering_matrix_and_get_information(fermi_energy, h00, h01, length=100): + import guan transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active = guan.calculate_scattering_matrix(fermi_energy, h00, h01, length=length) number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels = guan.information_of_scattering_matrix(transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active) @@ -1940,6 +2077,7 @@ def print_or_write_scattering_matrix_with_information_of_scattering_matrix(numbe # 已知h00和h01，计算散射矩阵并打印出散射矩阵的信息 def print_or_write_scattering_matrix(fermi_energy, h00, h01, length=100, print_show=1, write_file=0, filename='a', file_format='.txt'): + import guan transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active = guan.calculate_scattering_matrix(fermi_energy, h00, h01, length=length) number_of_active_channels, number_of_evanescent_channels, k_of_right_moving_active_channels, k_of_left_moving_active_channels, velocity_of_right_moving_active_channels, velocity_of_left_moving_active_channels, transmission_matrix_for_active_channels, reflection_matrix_for_active_channels, total_transmission_of_channels, total_conductance, total_reflection_of_channels, sum_of_transmission_and_reflection_of_channels = guan.information_of_scattering_matrix(transmission_matrix, reflection_matrix, k_right, k_left, velocity_right, velocity_left, ind_right_active) @@ -1948,7 +2086,10 @@ def print_or_write_scattering_matrix(fermi_energy, h00, h01, length=100, print_s # 在无序下，计算散射矩阵 def calculate_scattering_matrix_with_disorder(fermi_energy, h00, h01, length=100, disorder_intensity=2.0, disorder_concentration=1.0): + import numpy as np + import math import copy + import guan h01 = np.array(h01) if np.array(h00).shape==(): dim = 1 @@ -1994,6 +2135,7 @@ def calculate_scattering_matrix_with_disorder(fermi_energy, h00, h01, length=100 # 在无序下，计算散射矩阵，并获取散射矩阵多次计算的平均信息 def calculate_scattering_matrix_with_disorder_and_get_averaged_information(fermi_energy, h00, h01, length=100, disorder_intensity=2.0, disorder_concentration=1.0, calculation_times=1): + import guan transmission_matrix_for_active_channels_averaged = 0 reflection_matrix_for_active_channels_averaged = 0 for i0 in range(calculation_times): @@ -2076,6 +2218,10 @@ def calculate_scattering_matrix_with_disorder_and_get_averaged_information(fermi # 通过高效法计算方格子的陈数 def calculate_chern_number_for_square_lattice_with_efficient_method(hamiltonian_function, precision=100, print_show=0): + import numpy as np + import math + import cmath + import guan if np.array(hamiltonian_function(0, 0)).shape==(): dim = 1 else: @@ -2110,6 +2256,9 @@ def calculate_chern_number_for_square_lattice_with_efficient_method(hamiltonian_ # 通过高效法计算方格子的陈数（可计算简并的情况） def calculate_chern_number_for_square_lattice_with_efficient_method_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], precision=100, print_show=0): + import numpy as np + import math + import cmath delta = 2*math.pi/precision chern_number = 0 for kx in np.arange(-math.pi, math.pi, delta): @@ -2176,6 +2325,8 @@ def calculate_chern_number_for_square_lattice_with_efficient_method_for_degenera # 通过Wilson loop方法计算方格子的陈数 def calculate_chern_number_for_square_lattice_with_wilson_loop(hamiltonian_function, precision_of_plaquettes=20, precision_of_wilson_loop=5, print_show=0): + import numpy as np + import math delta = 2*math.pi/precision_of_plaquettes chern_number = 0 for kx in np.arange(-math.pi, math.pi, delta): @@ -2218,6 +2369,8 @@ def calculate_chern_number_for_square_lattice_with_wilson_loop(hamiltonian_funct # 通过Wilson loop方法计算方格子的陈数（可计算简并的情况） def 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): + import numpy as np + import math delta = 2*math.pi/precision_of_plaquettes chern_number = 0 for kx in np.arange(-math.pi, math.pi, delta): @@ -2278,7 +2431,11 @@ def calculate_chern_number_for_square_lattice_with_wilson_loop_for_degenerate_ca return chern_number # 通过高效法计算贝利曲率 +import math def calculate_berry_curvature_with_efficient_method(hamiltonian_function, k_min=-math.pi, k_max=math.pi, precision=100, print_show=0): + import numpy as np + import cmath + import guan if np.array(hamiltonian_function(0, 0)).shape==(): dim = 1 else: @@ -2316,7 +2473,10 @@ def calculate_berry_curvature_with_efficient_method(hamiltonian_function, k_min= return k_array, berry_curvature_array # 通过高效法计算贝利曲率（可计算简并的情况） +import math def calculate_berry_curvature_with_efficient_method_for_degenerate_case(hamiltonian_function, index_of_bands=[0, 1], k_min=-math.pi, k_max=math.pi, precision=100, print_show=0): + import numpy as np + import cmath 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]), dtype=complex) @@ -2387,7 +2547,9 @@ def calculate_berry_curvature_with_efficient_method_for_degenerate_case(hamilton return k_array, berry_curvature_array # 通过Wilson loop方法计算贝里曲率 +import math 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): + import numpy as np if np.array(hamiltonian_function(0, 0)).shape==(): dim = 1 else: @@ -2437,7 +2599,9 @@ def calculate_berry_curvature_with_wilson_loop(hamiltonian_function, k_min=-math return k_array, berry_curvature_array # 通过Wilson loop方法计算贝里曲率（可计算简并的情况） +import math 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): + import numpy as np 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) @@ -2503,6 +2667,10 @@ def calculate_berry_curvature_with_wilson_loop_for_degenerate_case(hamiltonian_f # 计算蜂窝格子的陈数（高效法） def calculate_chern_number_for_honeycomb_lattice(hamiltonian_function, a=1, precision=300, print_show=0): + import numpy as np + import math + import cmath + import guan if np.array(hamiltonian_function(0, 0)).shape==(): dim = 1 else: @@ -2541,7 +2709,10 @@ def calculate_chern_number_for_honeycomb_lattice(hamiltonian_function, a=1, prec return chern_number # 计算Wilson loop +import math def calculate_wilson_loop(hamiltonian_function, k_min=-math.pi, k_max=math.pi, precision=100, print_show=0): + import numpy as np + import guan k_array = np.linspace(k_min, k_max, precision) dim = np.array(hamiltonian_function(0)).shape[0] wilson_loop_array = np.ones(dim, dtype=complex) @@ -2653,6 +2824,7 @@ def plot_without_starting_fig(plt, fig, ax, x_array, y_array, xlabel='x', ylabel # 画图 def plot(x_array, y_array, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=20, show=1, save=0, filename='a', file_format='.jpg', dpi=300, style='', y_min=None, y_max=None, linewidth=None, markersize=None, adjust_bottom=0.2, adjust_left=0.2): + import guan plt, fig, ax = guan.import_plt_and_start_fig_ax(adjust_bottom=adjust_bottom, adjust_left=adjust_left, labelsize=labelsize) ax.plot(x_array, y_array, style, linewidth=linewidth, markersize=markersize) ax.set_title(title, fontsize=fontsize, fontfamily='Times New Roman') @@ -2672,6 +2844,7 @@ def plot(x_array, y_array, xlabel='x', ylabel='y', title='', fontsize=20, labels # 一组横坐标数据，两组纵坐标数据画图 def plot_two_array(x_array, y1_array, y2_array, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=20, show=1, save=0, filename='a', file_format='.jpg', dpi=300, style_1='', style_2='', y_min=None, y_max=None, linewidth_1=None, linewidth_2=None, markersize_1=None, markersize_2=None, adjust_bottom=0.2, adjust_left=0.2): + import guan plt, fig, ax = guan.import_plt_and_start_fig_ax(adjust_bottom=adjust_bottom, adjust_left=adjust_left, labelsize=labelsize) ax.plot(x_array, y1_array, style_1, linewidth=linewidth_1, markersize=markersize_1) ax.plot(x_array, y2_array, style_2, linewidth=linewidth_2, markersize=markersize_2) @@ -2696,6 +2869,7 @@ def plot_two_array(x_array, y1_array, y2_array, xlabel='x', ylabel='y', title='' # 两组横坐标数据，两组纵坐标数据画图 def plot_two_array_with_two_horizontal_array(x1_array, x2_array, y1_array, y2_array, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=20, show=1, save=0, filename='a', file_format='.jpg', dpi=300, style_1='', style_2='', y_min=None, y_max=None, linewidth_1=None, linewidth_2=None, markersize_1=None, markersize_2=None, adjust_bottom=0.2, adjust_left=0.2): + import guan plt, fig, ax = guan.import_plt_and_start_fig_ax(adjust_bottom=adjust_bottom, adjust_left=adjust_left, labelsize=labelsize) ax.plot(x1_array, y1_array, style_1, linewidth=linewidth_1, markersize=markersize_1) ax.plot(x2_array, y2_array, style_2, linewidth=linewidth_2, markersize=markersize_2) @@ -2720,6 +2894,7 @@ def plot_two_array_with_two_horizontal_array(x1_array, x2_array, y1_array, y2_ar # 一组横坐标数据，三组纵坐标数据画图 def plot_three_array(x_array, y1_array, y2_array, y3_array, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=20, show=1, save=0, filename='a', file_format='.jpg', dpi=300, style_1='', style_2='', style_3='', y_min=None, y_max=None, linewidth_1=None, linewidth_2=None, linewidth_3=None,markersize_1=None, markersize_2=None, markersize_3=None, adjust_bottom=0.2, adjust_left=0.2): + import guan plt, fig, ax = guan.import_plt_and_start_fig_ax(adjust_bottom=adjust_bottom, adjust_left=adjust_left, labelsize=labelsize) ax.plot(x_array, y1_array, style_1, linewidth=linewidth_1, markersize=markersize_1) ax.plot(x_array, y2_array, style_2, linewidth=linewidth_2, markersize=markersize_2) @@ -2747,6 +2922,7 @@ def plot_three_array(x_array, y1_array, y2_array, y3_array, xlabel='x', ylabel=' # 三组横坐标数据，三组纵坐标数据画图 def plot_three_array_with_three_horizontal_array(x1_array, x2_array, x3_array, y1_array, y2_array, y3_array, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=20, show=1, save=0, filename='a', file_format='.jpg', dpi=300, style_1='', style_2='', style_3='', y_min=None, y_max=None, linewidth_1=None, linewidth_2=None, linewidth_3=None,markersize_1=None, markersize_2=None, markersize_3=None, adjust_bottom=0.2, adjust_left=0.2): + import guan plt, fig, ax = guan.import_plt_and_start_fig_ax(adjust_bottom=adjust_bottom, adjust_left=adjust_left, labelsize=labelsize) ax.plot(x1_array, y1_array, style_1, linewidth=linewidth_1, markersize=markersize_1) ax.plot(x2_array, y2_array, style_2, linewidth=linewidth_2, markersize=markersize_2) @@ -2774,6 +2950,7 @@ def plot_three_array_with_three_horizontal_array(x1_array, x2_array, x3_array, y # 画三维图 def plot_3d_surface(x_array, y_array, matrix, xlabel='x', ylabel='y', zlabel='z', title='', fontsize=20, labelsize=15, show=1, save=0, filename='a', file_format='.jpg', dpi=300, z_min=None, z_max=None, rcount=100, ccount=100): + import numpy as np import matplotlib.pyplot as plt from matplotlib import cm from matplotlib.ticker import LinearLocator @@ -2813,7 +2990,8 @@ def plot_3d_surface(x_array, y_array, matrix, xlabel='x', ylabel='y', zlabel='z' plt.close('all') # 画Contour图 -def plot_contour(x_array, y_array, matrix, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=15, cmap='jet', levels=None, show=1, save=0, filename='a', file_format='.jpg', dpi=300): +def plot_contour(x_array, y_array, matrix, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=15, cmap='jet', levels=None, show=1, save=0, filename='a', file_format='.jpg', dpi=300): + import numpy as np import matplotlib.pyplot as plt fig, ax = plt.subplots() plt.subplots_adjust(bottom=0.2, right=0.75, left=0.2) @@ -2838,6 +3016,7 @@ def plot_contour(x_array, y_array, matrix, xlabel='x', ylabel='y', title='', fon # 画棋盘图/伪彩色图 def plot_pcolor(x_array, y_array, matrix, xlabel='x', ylabel='y', title='', fontsize=20, labelsize=15, cmap='jet', levels=None, show=1, save=0, filename='a', file_format='.jpg', dpi=300): + import numpy as np import matplotlib.pyplot as plt fig, ax = plt.subplots() plt.subplots_adjust(bottom=0.2, right=0.75, left=0.2) @@ -2862,6 +3041,7 @@ def plot_pcolor(x_array, y_array, matrix, xlabel='x', ylabel='y', title='', font # 通过坐标画点和线 def draw_dots_and_lines(coordinate_array, draw_dots=1, draw_lines=1, max_distance=1.1, line_style='-k', linewidth=1, dot_style='ro', markersize=3, show=1, save=0, filename='a', file_format='.eps', dpi=300): + import numpy as np import matplotlib.pyplot as plt coordinate_array = np.array(coordinate_array) print(coordinate_array.shape) @@ -2888,6 +3068,7 @@ def draw_dots_and_lines(coordinate_array, draw_dots=1, draw_lines=1, max_distanc # 合并两个图片 def combine_two_images(image_path_array, figsize=(16,8), show=0, save=1, filename='a', file_format='.jpg', dpi=300): + import numpy as np num = np.array(image_path_array).shape[0] if num != 2: print('Error: The number of images should be two!') @@ -2912,6 +3093,7 @@ def combine_two_images(image_path_array, figsize=(16,8), show=0, save=1, filenam # 合并三个图片 def combine_three_images(image_path_array, figsize=(16,5), show=0, save=1, filename='a', file_format='.jpg', dpi=300): + import numpy as np num = np.array(image_path_array).shape[0] if num != 3: print('Error: The number of images should be three!') @@ -2940,6 +3122,7 @@ def combine_three_images(image_path_array, figsize=(16,5), show=0, save=1, filen # 合并四个图片 def combine_four_images(image_path_array, figsize=(16,16), show=0, save=1, filename='a', file_format='.jpg', dpi=300): + import numpy as np num = np.array(image_path_array).shape[0] if num != 4: print('Error: The number of images should be four!') @@ -3062,11 +3245,12 @@ def dump_data(data, filename, file_format='.txt'): def load_data(filename, file_format='.txt'): import pickle with open(filename+file_format, 'rb') as f: - data = pickle.load(f) + data = pickle.load(f) return data # 读取文件中的一维数据（每一行一组x和y） def read_one_dimensional_data(filename='a', file_format='.txt'): + import numpy as np f = open(filename+file_format, 'r') text = f.read() f.close() @@ -3089,6 +3273,7 @@ def read_one_dimensional_data(filename='a', file_format='.txt'): # 读取文件中的一维数据（每一行一组x和y）（支持复数形式） def read_one_dimensional_complex_data(filename='a', file_format='.txt'): + import numpy as np f = open(filename+file_format, 'r') text = f.read() f.close() @@ -3111,6 +3296,7 @@ def read_one_dimensional_complex_data(filename='a', file_format='.txt'): # 读取文件中的二维数据（第一行和列分别为横纵坐标） def read_two_dimensional_data(filename='a', file_format='.txt'): + import numpy as np f = open(filename+file_format, 'r') text = f.read() f.close() @@ -3139,6 +3325,7 @@ def read_two_dimensional_data(filename='a', file_format='.txt'): # 读取文件中的二维数据（第一行和列分别为横纵坐标）（支持复数形式） def read_two_dimensional_complex_data(filename='a', file_format='.txt'): + import numpy as np f = open(filename+file_format, 'r') text = f.read() f.close() @@ -3167,6 +3354,7 @@ def read_two_dimensional_complex_data(filename='a', file_format='.txt'): # 读取文件中的二维数据（不包括x和y） def read_two_dimensional_data_without_xy_array(filename='a', file_format='.txt'): + import numpy as np matrix = np.loadtxt(filename+file_format) return matrix @@ -3179,12 +3367,14 @@ def open_file(filename='a', file_format='.txt'): return f # 在文件中写入一维数据（每一行一组x和y） -def write_one_dimensional_data(x_array, y_array, filename='a', file_format='.txt'): +def write_one_dimensional_data(x_array, y_array, filename='a', file_format='.txt'): + import guan with open(filename+file_format, 'w', encoding='UTF-8') as f: guan.write_one_dimensional_data_without_opening_file(x_array, y_array, f) # 在文件中写入一维数据（每一行一组x和y）（需要输入文件） -def write_one_dimensional_data_without_opening_file(x_array, y_array, f): +def write_one_dimensional_data_without_opening_file(x_array, y_array, f): + import numpy as np x_array = np.array(x_array) y_array = np.array(y_array) i0 = 0 @@ -3199,12 +3389,14 @@ def write_one_dimensional_data_without_opening_file(x_array, y_array, f): i0 += 1 # 在文件中写入二维数据（第一行和列分别为横纵坐标） -def write_two_dimensional_data(x_array, y_array, matrix, filename='a', file_format='.txt'): +def write_two_dimensional_data(x_array, y_array, matrix, filename='a', file_format='.txt'): + import guan with open(filename+file_format, 'w', encoding='UTF-8') as f: guan.write_two_dimensional_data_without_opening_file(x_array, y_array, matrix, f) # 在文件中写入二维数据（第一行和列分别为横纵坐标）（需要输入文件） -def write_two_dimensional_data_without_opening_file(x_array, y_array, matrix, f): +def write_two_dimensional_data_without_opening_file(x_array, y_array, matrix, f): + import numpy as np x_array = np.array(x_array) y_array = np.array(y_array) matrix = np.array(matrix) @@ -3224,6 +3416,7 @@ def write_two_dimensional_data_without_opening_file(x_array, y_array, matrix, f) # 在文件中写入二维数据（不包括x和y） def write_two_dimensional_data_without_xy_array(matrix, filename='a', file_format='.txt'): + import guan with open(filename+file_format, 'w', encoding='UTF-8') as f: guan.write_two_dimensional_data_without_xy_array_and_without_opening_file(matrix, f) @@ -3307,6 +3500,7 @@ def print_array_with_index(array, show_index=1, index_type=0): # 并行计算前的预处理，把参数分成多份 def preprocess_for_parallel_calculations(parameter_array_all, cpus=1, task_index=0): + import numpy as np num_all = np.array(parameter_array_all).shape[0] if num_all%cpus == 0: num_parameter = int(num_all/cpus) @@ -3334,11 +3528,12 @@ def find_close_values_in_one_array(array, precision=1e-2): # 寻找能带的简并点 def find_degenerate_points(k_array, eigenvalue_array, precision=1e-2): + import guan degenerate_k_array = [] degenerate_eigenvalue_array = [] i0 = 0 for k in k_array: - degenerate_points = find_close_values_in_one_array(eigenvalue_array[i0], precision=precision) + degenerate_points = guan.find_close_values_in_one_array(eigenvalue_array[i0], precision=precision) if len(degenerate_points) != 0: degenerate_k_array.append(k) degenerate_eigenvalue_array.append(degenerate_points) @@ -3349,6 +3544,7 @@ def find_degenerate_points(k_array, eigenvalue_array, precision=1e-2): def batch_reading_and_plotting(directory, xlabel='x', ylabel='y'): import re import os + import guan for root, dirs, files in os.walk(directory): for file in files: if re.search('^txt.', file[::-1]): @@ -3400,6 +3596,7 @@ def get_time(): # 获取所有股票 def all_stocks(): + import numpy as np import akshare as ak stocks = ak.stock_zh_a_spot_em() title = np.array(stocks.columns) @@ -3408,12 +3605,14 @@ def all_stocks(): # 获取所有股票的代码 def all_stock_symbols(): + import guan title, stock_data = guan.all_stocks() stock_symbols = stock_data[:, 1] return stock_symbols # 从股票代码获取股票名称 def find_stock_name_from_symbol(symbol='000002'): + import guan title, stock_data = guan.all_stocks() for stock in stock_data: if symbol in stock: @@ -3425,6 +3624,7 @@ def history_data_of_one_stock(symbol='000002', period='daily', start_date="19000 # period = 'daily' # period = 'weekly' # period = 'monthly' + import numpy as np import akshare as ak stock = ak.stock_zh_a_hist(symbol=symbol, period=period, start_date=start_date, end_date=end_date) title = np.array(stock.columns) @@ -3983,6 +4183,7 @@ def creat_qrcode(data="https://www.guanjihuan.com", filename='a', file_format='. # 将文本转成音频 def str_to_audio(str='hello world', filename='str', rate=125, voice=1, read=1, save=0, compress=0, bitrate='16k', print_text=0): import pyttsx3 + import guan if print_text==1: print(str) engine = pyttsx3.init() @@ -4005,6 +4206,7 @@ def str_to_audio(str='hello world', filename='str', rate=125, voice=1, read=1, s # 将txt文件转成音频 def txt_to_audio(txt_path, rate=125, voice=1, read=1, save=0, compress=0, bitrate='16k', print_text=0): import pyttsx3 + import guan f = open(txt_path, 'r', encoding ='utf-8') text = f.read() if print_text==1: @@ -4031,6 +4233,7 @@ def txt_to_audio(txt_path, rate=125, voice=1, read=1, save=0, compress=0, bitrat # 将PDF文件转成音频 def pdf_to_audio(pdf_path, rate=125, voice=1, read=1, save=0, compress=0, bitrate='16k', print_text=0): import pyttsx3 + import guan text = guan.pdf_to_text(pdf_path) text = text.replace('\n', ' ') if print_text==1: