239 lines
8.3 KiB
Plaintext
239 lines
8.3 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "4f66c596-dc32-4b03-bf34-726a206eaff5",
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"metadata": {},
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"outputs": [],
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"source": [
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"# GUAN软件包官网: https://py.guanjihuan.com\n",
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"import guan\n",
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"guan.test()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "214d56d6-1626-4fce-bc7d-9084c74cf4fc",
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"metadata": {},
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"outputs": [],
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"source": [
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"# 泡利矩阵\n",
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"import guan\n",
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"sigma_x = guan.sigma_x()\n",
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"print(sigma_x)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "f8727100-fab6-487c-9d50-a9390aabe623",
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"metadata": {},
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"outputs": [],
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"source": [
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"# 函数的计时器\n",
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"import guan\n",
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"\n",
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"@guan.timer_decorator\n",
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"def my_function():\n",
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" import time\n",
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" time.sleep(2)\n",
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" print('Run finished！')\n",
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"\n",
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"for _ in range(3):\n",
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" my_function()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "2778f460-f8c9-496e-a003-59394379bb20",
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"metadata": {},
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"outputs": [],
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"source": [
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"# 实空间哈密顿量的示例\n",
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"import guan\n",
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"print('\\n', guan.hamiltonian_of_finite_size_system_along_one_direction(3), '\\n')\n",
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"print(guan.hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(2, 2), '\\n')\n",
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"print(guan.hamiltonian_of_finite_size_system_along_three_directions_for_cubic_lattice(2, 2, 2), '\\n')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "a08fb5f1-724c-43b1-ad4a-daa94b9f1605",
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"metadata": {},
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"outputs": [],
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"source": [
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"# 能带图计算示例\n",
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"import guan\n",
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"import numpy as np\n",
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"k_array = np.linspace(-np.pi, np.pi, 100)\n",
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" # one dimensional chain\n",
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"hamiltonian_function = guan.one_dimensional_fourier_transform_with_k(unit_cell=0, hopping=1)\n",
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"eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, hamiltonian_function)\n",
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"guan.plot(k_array, eigenvalue_array, xlabel='k', ylabel='E', style='-k', fontfamily=None)\n",
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"# square lattice ribbon\n",
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"eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, guan.hamiltonian_of_square_lattice_in_quasi_one_dimension)\n",
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"guan.plot(k_array, eigenvalue_array, xlabel='k', ylabel='E', style='-k', fontfamily=None)\n",
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"# graphene ribbon\n",
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"eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, guan.hamiltonian_of_graphene_with_zigzag_in_quasi_one_dimension)\n",
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"guan.plot(k_array, eigenvalue_array, xlabel='k', ylabel='E', style='-k', fontfamily=None)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "adc6a47a-8b4f-416f-8bca-65ee2b068fb9",
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"metadata": {},
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"outputs": [],
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"source": [
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"# 陈数和Wilson loop计算示例\n",
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"import guan\n",
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"import numpy as np\n",
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"chern_number = guan.calculate_chern_number_for_square_lattice_with_efficient_method(guan.hamiltonian_of_one_QAH_model, precision=100)\n",
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"print('\\nChern number=', chern_number, '\\n')\n",
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"wilson_loop_array = guan.calculate_wilson_loop(guan.hamiltonian_of_ssh_model)\n",
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"print('Wilson loop =', wilson_loop_array)\n",
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"p = np.log(wilson_loop_array)/2/np.pi/1j\n",
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"print('\\np =', p, '\\n')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "44aa1ca5-ca8b-4afc-a719-d40736edeee5",
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"metadata": {},
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"outputs": [],
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"source": [
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"# 使用格林函数计算态密度示例\n",
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"import guan\n",
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"import numpy as np\n",
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"\n",
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"hamiltonian = guan.hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(2,2)\n",
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"fermi_energy_array = np.linspace(-4, 4, 400)\n",
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"total_dos_array = guan.total_density_of_states_with_fermi_energy_array(fermi_energy_array, hamiltonian, broadening=0.1)\n",
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"guan.plot(fermi_energy_array, total_dos_array, xlabel='E', ylabel='Total DOS', style='-', fontfamily=None)\n",
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"\n",
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"fermi_energy = 0\n",
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"N1 = 3\n",
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"N2 = 4\n",
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"hamiltonian = guan.hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(N1,N2)\n",
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"LDOS = guan.local_density_of_states_for_square_lattice(fermi_energy, hamiltonian, N1=N1, N2=N2)\n",
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"print('square lattice:\\n', LDOS, '\\n')\n",
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"h00 = guan.hamiltonian_of_finite_size_system_along_one_direction(N2)\n",
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"h01 = np.identity(N2)\n",
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"LDOS = guan.local_density_of_states_for_square_lattice_using_dyson_equation(fermi_energy, h00=h00, h01=h01, N2=N2, N1=N1)\n",
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"print(LDOS, '\\n\\n')\n",
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"LDOS2 = guan.local_density_of_states_for_square_lattice_using_dyson_equation_with_second_method(fermi_energy, h00, h01, N2, N1, internal_degree=1, broadening=0.01)\n",
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"print(LDOS2, '\\n\\n')\n",
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"guan.plot_contour(range(N1), range(N2), LDOS, fontfamily=None)\n",
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"guan.plot_contour(range(N1), range(N2), LDOS2, fontfamily=None)\n",
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"\n",
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"N1 = 3\n",
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"N2 = 4\n",
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"N3 = 5\n",
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"hamiltonian = guan.hamiltonian_of_finite_size_system_along_three_directions_for_cubic_lattice(N1, N2, N3)\n",
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"LDOS = guan.local_density_of_states_for_cubic_lattice(fermi_energy, hamiltonian, N1=N1, N2=N2, N3=N3)\n",
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"print('cubic lattice:\\n', LDOS, '\\n')\n",
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"h00 = guan.hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(N2, N3)\n",
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"h01 = np.identity(N2*N3)\n",
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"LDOS = guan.local_density_of_states_for_cubic_lattice_using_dyson_equation(fermi_energy, h00, h01, N3=N3, N2=N2, N1=N1)\n",
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"print(LDOS)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "cdfd4123-dcb2-4dc5-9e48-a35728fd7168",
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"metadata": {},
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"outputs": [],
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"source": [
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"# 电导和散射矩阵的计算示例\n",
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"import guan\n",
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"import numpy as np\n",
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"\n",
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"fermi_energy_array = np.linspace(-4, 4, 400)\n",
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"h00 = guan.hamiltonian_of_finite_size_system_along_one_direction(4)\n",
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"h01 = np.identity(4)\n",
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"conductance_array = guan.calculate_conductance_with_fermi_energy_array(fermi_energy_array, h00, h01)\n",
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"guan.plot(fermi_energy_array, conductance_array, xlabel='E', ylabel='Conductance', style='-', fontfamily=None)\n",
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"\n",
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"fermi_energy = 0\n",
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"guan.print_or_write_scattering_matrix(fermi_energy, h00, h01)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "fd0f2bcc-82cd-4951-8b4b-e6913d767008",
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"metadata": {},
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"outputs": [],
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"source": [
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"# 波函数规范的选取示例\n",
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"import numpy as np\n",
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"import cmath\n",
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"import guan\n",
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"\n",
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"# Fixed gauge example 1\n",
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"vector = np.array([np.sqrt(0.5), np.sqrt(0.5)])*cmath.exp(np.random.uniform(0, 1)*1j)\n",
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"print('\\nExample 1\\n', vector)\n",
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"print(np.dot(vector.transpose().conj(), vector), '\\n')\n",
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"\n",
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"vector = guan.find_vector_with_fixed_gauge_by_making_one_component_real(vector)\n",
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"print(vector)\n",
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"print(np.dot(vector.transpose().conj(), vector), '\\n')\n",
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"\n",
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"# Fixed gauge example 2\n",
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"vector = np.array([1, 0])*cmath.exp(np.random.uniform(0, 1)*1j)\n",
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"print('\\nExample 2\\n', vector)\n",
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"print(np.dot(vector.transpose().conj(), vector), '\\n')\n",
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"\n",
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"vector = guan.find_vector_with_fixed_gauge_by_making_one_component_real(vector)\n",
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"print(vector)\n",
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"print(np.dot(vector.transpose().conj(), vector), '\\n')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "444c5848-c50d-4fb3-b71c-056b5005620b",
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"metadata": {},
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"outputs": [],
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"source": [
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"# 数组分割示例\n",
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"import numpy as np\n",
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"import guan\n",
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"cpus = 4\n",
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"parameter_array_all = np.arange(0, 17, 1) \n",
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"for task_index in range(cpus):\n",
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" parameter_array = guan.preprocess_for_parallel_calculations(parameter_array_all, cpus, task_index)\n",
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" print(parameter_array)\n",
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" print()"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.7"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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