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2024-04-02 13:53:11 +08:00
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2024.01.16_GUAN_package_learning/GUAN_package_learning.ipynb
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{
"cells": [
{
"cell_type": "code",
"execution_count": null,
"id": "4f66c596-dc32-4b03-bf34-726a206eaff5",
"metadata": {},
"outputs": [],
"source": [
"# GUAN软件包官网: https://py.guanjihuan.com\n",
"import guan\n",
"guan.test()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "214d56d6-1626-4fce-bc7d-9084c74cf4fc",
"metadata": {},
"outputs": [],
"source": [
"# 泡利矩阵\n",
"import guan\n",
"sigma_x = guan.sigma_x()\n",
"print(sigma_x)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f8727100-fab6-487c-9d50-a9390aabe623",
"metadata": {},
"outputs": [],
"source": [
"# 函数的计时器\n",
"import guan\n",
"\n",
"@guan.timer_decorator\n",
"def my_function():\n",
" import time\n",
" time.sleep(2)\n",
" print('Run finished！')\n",
"\n",
"for _ in range(3):\n",
" my_function()"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "2778f460-f8c9-496e-a003-59394379bb20",
"metadata": {},
"outputs": [],
"source": [
"# 实空间哈密顿量的示例\n",
"import guan\n",
"print('\\n', guan.hamiltonian_of_finite_size_system_along_one_direction(3), '\\n')\n",
"print(guan.hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(2, 2), '\\n')\n",
"print(guan.hamiltonian_of_finite_size_system_along_three_directions_for_cubic_lattice(2, 2, 2), '\\n')"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a08fb5f1-724c-43b1-ad4a-daa94b9f1605",
"metadata": {},
"outputs": [],
"source": [
"# 能带图计算示例\n",
"import guan\n",
"import numpy as np\n",
"k_array = np.linspace(-np.pi, np.pi, 100)\n",
" # one dimensional chain\n",
"hamiltonian_function = guan.one_dimensional_fourier_transform_with_k(unit_cell=0, hopping=1)\n",
"eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, hamiltonian_function)\n",
"guan.plot(k_array, eigenvalue_array, xlabel='k', ylabel='E', style='-k', fontfamily=None)\n",
"# square lattice ribbon\n",
"eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, guan.hamiltonian_of_square_lattice_in_quasi_one_dimension)\n",
"guan.plot(k_array, eigenvalue_array, xlabel='k', ylabel='E', style='-k', fontfamily=None)\n",
"# graphene ribbon\n",
"eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, guan.hamiltonian_of_graphene_with_zigzag_in_quasi_one_dimension)\n",
"guan.plot(k_array, eigenvalue_array, xlabel='k', ylabel='E', style='-k', fontfamily=None)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "adc6a47a-8b4f-416f-8bca-65ee2b068fb9",
"metadata": {},
"outputs": [],
"source": [
"# 陈数和Wilson loop计算示例\n",
"import guan\n",
"import numpy as np\n",
"chern_number = guan.calculate_chern_number_for_square_lattice_with_efficient_method(guan.hamiltonian_of_one_QAH_model, precision=100)\n",
"print('\\nChern number=', chern_number, '\\n')\n",
"wilson_loop_array = guan.calculate_wilson_loop(guan.hamiltonian_of_ssh_model)\n",
"print('Wilson loop =', wilson_loop_array)\n",
"p = np.log(wilson_loop_array)/2/np.pi/1j\n",
"print('\\np =', p, '\\n')"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "44aa1ca5-ca8b-4afc-a719-d40736edeee5",
"metadata": {},
"outputs": [],
"source": [
"# 使用格林函数计算态密度示例\n",
"import guan\n",
"import numpy as np\n",
"\n",
"hamiltonian = guan.hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(2,2)\n",
"fermi_energy_array = np.linspace(-4, 4, 400)\n",
"total_dos_array = guan.total_density_of_states_with_fermi_energy_array(fermi_energy_array, hamiltonian, broadening=0.1)\n",
"guan.plot(fermi_energy_array, total_dos_array, xlabel='E', ylabel='Total DOS', style='-', fontfamily=None)\n",
"\n",
"fermi_energy = 0\n",
"N1 = 3\n",
"N2 = 4\n",
"hamiltonian = guan.hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(N1,N2)\n",
"LDOS = guan.local_density_of_states_for_square_lattice(fermi_energy, hamiltonian, N1=N1, N2=N2)\n",
"print('square lattice:\\n', LDOS, '\\n')\n",
"h00 = guan.hamiltonian_of_finite_size_system_along_one_direction(N2)\n",
"h01 = np.identity(N2)\n",
"LDOS = guan.local_density_of_states_for_square_lattice_using_dyson_equation(fermi_energy, h00=h00, h01=h01, N2=N2, N1=N1)\n",
"print(LDOS, '\\n\\n')\n",
"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",
"print(LDOS2, '\\n\\n')\n",
"guan.plot_contour(range(N1), range(N2), LDOS, fontfamily=None)\n",
"guan.plot_contour(range(N1), range(N2), LDOS2, fontfamily=None)\n",
"\n",
"N1 = 3\n",
"N2 = 4\n",
"N3 = 5\n",
"hamiltonian = guan.hamiltonian_of_finite_size_system_along_three_directions_for_cubic_lattice(N1, N2, N3)\n",
"LDOS = guan.local_density_of_states_for_cubic_lattice(fermi_energy, hamiltonian, N1=N1, N2=N2, N3=N3)\n",
"print('cubic lattice:\\n', LDOS, '\\n')\n",
"h00 = guan.hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(N2, N3)\n",
"h01 = np.identity(N2*N3)\n",
"LDOS = guan.local_density_of_states_for_cubic_lattice_using_dyson_equation(fermi_energy, h00, h01, N3=N3, N2=N2, N1=N1)\n",
"print(LDOS)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "cdfd4123-dcb2-4dc5-9e48-a35728fd7168",
"metadata": {},
"outputs": [],
"source": [
"# 电导和散射矩阵的计算示例\n",
"import guan\n",
"import numpy as np\n",
"\n",
"fermi_energy_array = np.linspace(-4, 4, 400)\n",
"h00 = guan.hamiltonian_of_finite_size_system_along_one_direction(4)\n",
"h01 = np.identity(4)\n",
"conductance_array = guan.calculate_conductance_with_fermi_energy_array(fermi_energy_array, h00, h01)\n",
"guan.plot(fermi_energy_array, conductance_array, xlabel='E', ylabel='Conductance', style='-', fontfamily=None)\n",
"\n",
"fermi_energy = 0\n",
"guan.print_or_write_scattering_matrix(fermi_energy, h00, h01)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "fd0f2bcc-82cd-4951-8b4b-e6913d767008",
"metadata": {},
"outputs": [],
"source": [
"# 波函数规范的选取示例\n",
"import numpy as np\n",
"import cmath\n",
"import guan\n",
"\n",
"# Fixed gauge example 1\n",
"vector = np.array([np.sqrt(0.5), np.sqrt(0.5)])*cmath.exp(np.random.uniform(0, 1)*1j)\n",
"print('\\nExample 1\\n', vector)\n",
"print(np.dot(vector.transpose().conj(), vector), '\\n')\n",
"\n",
"vector = guan.find_vector_with_fixed_gauge_by_making_one_component_real(vector)\n",
"print(vector)\n",
"print(np.dot(vector.transpose().conj(), vector), '\\n')\n",
"\n",
"# Fixed gauge example 2\n",
"vector = np.array([1, 0])*cmath.exp(np.random.uniform(0, 1)*1j)\n",
"print('\\nExample 2\\n', vector)\n",
"print(np.dot(vector.transpose().conj(), vector), '\\n')\n",
"\n",
"vector = guan.find_vector_with_fixed_gauge_by_making_one_component_real(vector)\n",
"print(vector)\n",
"print(np.dot(vector.transpose().conj(), vector), '\\n')"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "444c5848-c50d-4fb3-b71c-056b5005620b",
"metadata": {},
"outputs": [],
"source": [
"# 数组分割示例\n",
"import numpy as np\n",
"import guan\n",
"cpus = 4\n",
"parameter_array_all = np.arange(0, 17, 1) \n",
"for task_index in range(cpus):\n",
" parameter_array = guan.preprocess_for_parallel_calculations(parameter_array_all, cpus, task_index)\n",
" print(parameter_array)\n",
" print()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.7"
}
},
"nbformat": 4,
"nbformat_minor": 5
}

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2024.01.16_GUAN_package_learning/example_of_array_division.py Normal file
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# 数组分割示例
import numpy as np
import guan
cpus = 4
parameter_array_all = np.arange(0, 17, 1)
for task_index in range(cpus):
parameter_array = guan.preprocess_for_parallel_calculations(parameter_array_all, cpus, task_index)
print(parameter_array)
print()

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2024.01.16_GUAN_package_learning/example_of_band_structure.py Normal file
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# 能带图计算示例
import guan
import numpy as np
k_array = np.linspace(-np.pi, np.pi, 100)
# one dimensional chain
hamiltonian_function = guan.one_dimensional_fourier_transform_with_k(unit_cell=0, hopping=1)
eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, hamiltonian_function)
guan.plot(k_array, eigenvalue_array, xlabel='k', ylabel='E', style='-k', fontfamily=None)
# square lattice ribbon
eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, guan.hamiltonian_of_square_lattice_in_quasi_one_dimension)
guan.plot(k_array, eigenvalue_array, xlabel='k', ylabel='E', style='-k', fontfamily=None)
# graphene ribbon
eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, guan.hamiltonian_of_graphene_with_zigzag_in_quasi_one_dimension)
guan.plot(k_array, eigenvalue_array, xlabel='k', ylabel='E', style='-k', fontfamily=None)

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2024.01.16_GUAN_package_learning/example_of_chern_number_and_wilson_loop.py Normal file
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# 陈数和Wilson loop计算示例
import guan
import numpy as np
chern_number = guan.calculate_chern_number_for_square_lattice_with_efficient_method(guan.hamiltonian_of_one_QAH_model, precision=100)
print('\nChern number=', chern_number, '\n')
wilson_loop_array = guan.calculate_wilson_loop(guan.hamiltonian_of_ssh_model)
print('Wilson loop =', wilson_loop_array)
p = np.log(wilson_loop_array)/2/np.pi/1j
print('\np =', p, '\n')

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2024.01.16_GUAN_package_learning/example_of_conductance_and_scattering_matrix.py Normal file
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# 电导和散射矩阵的计算示例
import guan
import numpy as np
fermi_energy_array = np.linspace(-4, 4, 400)
h00 = guan.hamiltonian_of_finite_size_system_along_one_direction(4)
h01 = np.identity(4)
conductance_array = guan.calculate_conductance_with_fermi_energy_array(fermi_energy_array, h00, h01)
guan.plot(fermi_energy_array, conductance_array, xlabel='E', ylabel='Conductance', style='-', fontfamily=None)
fermi_energy = 0
guan.print_or_write_scattering_matrix(fermi_energy, h00, h01)

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2024.01.16_GUAN_package_learning/example_of_dos_calculation.py Normal file
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# 使用格林函数计算态密度示例
import guan
import numpy as np
hamiltonian = guan.hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(2,2)
fermi_energy_array = np.linspace(-4, 4, 400)
total_dos_array = guan.total_density_of_states_with_fermi_energy_array(fermi_energy_array, hamiltonian, broadening=0.1)
guan.plot(fermi_energy_array, total_dos_array, xlabel='E', ylabel='Total DOS', style='-', fontfamily=None)
fermi_energy = 0
N1 = 3
N2 = 4
hamiltonian = guan.hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(N1,N2)
LDOS = guan.local_density_of_states_for_square_lattice(fermi_energy, hamiltonian, N1=N1, N2=N2)
print('square lattice:\n', LDOS, '\n')
h00 = guan.hamiltonian_of_finite_size_system_along_one_direction(N2)
h01 = np.identity(N2)
LDOS = guan.local_density_of_states_for_square_lattice_using_dyson_equation(fermi_energy, h00=h00, h01=h01, N2=N2, N1=N1)
print(LDOS, '\n\n')
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)
print(LDOS2, '\n\n')
guan.plot_contour(range(N1), range(N2), LDOS, fontfamily=None)
guan.plot_contour(range(N1), range(N2), LDOS2, fontfamily=None)
N1 = 3
N2 = 4
N3 = 5
hamiltonian = guan.hamiltonian_of_finite_size_system_along_three_directions_for_cubic_lattice(N1, N2, N3)
LDOS = guan.local_density_of_states_for_cubic_lattice(fermi_energy, hamiltonian, N1=N1, N2=N2, N3=N3)
print('cubic lattice:\n', LDOS, '\n')
h00 = guan.hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(N2, N3)
h01 = np.identity(N2*N3)
LDOS = guan.local_density_of_states_for_cubic_lattice_using_dyson_equation(fermi_energy, h00, h01, N3=N3, N2=N2, N1=N1)
print(LDOS)

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2024.01.16_GUAN_package_learning/example_of_gauge_fixing.py Normal file
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# 波函数规范的选取示例
import numpy as np
import cmath
import guan
# Fixed gauge example 1
vector = np.array([np.sqrt(0.5), np.sqrt(0.5)])*cmath.exp(np.random.uniform(0, 1)*1j)
print('\nExample 1\n', vector)
print(np.dot(vector.transpose().conj(), vector), '\n')
vector = guan.find_vector_with_fixed_gauge_by_making_one_component_real(vector)
print(vector)
print(np.dot(vector.transpose().conj(), vector), '\n')
# Fixed gauge example 2
vector = np.array([1, 0])*cmath.exp(np.random.uniform(0, 1)*1j)
print('\nExample 2\n', vector)
print(np.dot(vector.transpose().conj(), vector), '\n')
vector = guan.find_vector_with_fixed_gauge_by_making_one_component_real(vector)
print(vector)
print(np.dot(vector.transpose().conj(), vector), '\n')

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2024.01.16_GUAN_package_learning/example_of_hamiltonian_in_real_space.py Normal file
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# 实空间哈密顿量的示例
import guan
print('\n', guan.hamiltonian_of_finite_size_system_along_one_direction(3), '\n')
print(guan.hamiltonian_of_finite_size_system_along_two_directions_for_square_lattice(2, 2), '\n')
print(guan.hamiltonian_of_finite_size_system_along_three_directions_for_cubic_lattice(2, 2, 2), '\n')

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2024.01.16_GUAN_package_learning/pauli_matrix.py Normal file
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# 泡利矩阵
import guan
sigma_x = guan.sigma_x()
print(sigma_x)

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2024.01.16_GUAN_package_learning/test.py Normal file
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# GUAN软件包官网: https://py.guanjihuan.com
import guan
guan.test()

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2024.01.16_GUAN_package_learning/timer.py Normal file
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# 函数的计时器
import guan
@guan.timer_decorator
def my_function():
import time
time.sleep(2)
print('Run finished！')
for _ in range(3):
my_function()