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calculate_chern_number_for_square_lattice_with_Wilson_loop

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guanjihuan
2022-01-11 06:13:37 +08:00
parent c2409871c9
commit 44ea172ead
4 changed files with 45 additions and 4 deletions
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1
API_reference.py
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@@ -99,6 +99,7 @@ guan.print_or_write_scattering_matrix(fermi_energy, h00, h01, length=100, on_pri
# calculate topological invariant # Source code: https://py.guanjihuan.com/source-code/calculate_topological_invariant # calculate topological invariant # Source code: https://py.guanjihuan.com/source-code/calculate_topological_invariant
chern_number = guan.calculate_chern_number_for_square_lattice(hamiltonian_function, precision=100) chern_number = guan.calculate_chern_number_for_square_lattice(hamiltonian_function, precision=100)
chern_number = guan.calculate_chern_number_for_square_lattice_with_Wilson_loop(hamiltonian_function, precision_of_plaquettes=10, precision_of_Wilson_loop=100)
chern_number = guan.calculate_chern_number_for_honeycomb_lattice(hamiltonian_function, a=1, precision=300) chern_number = guan.calculate_chern_number_for_honeycomb_lattice(hamiltonian_function, a=1, precision=300)
wilson_loop_array = guan.calculate_wilson_loop(hamiltonian_function, k_min=-pi, k_max=pi, precision=100) wilson_loop_array = guan.calculate_wilson_loop(hamiltonian_function, k_min=-pi, k_max=pi, precision=100)

2
PyPI/setup.cfg
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@@ -1,7 +1,7 @@
[metadata] [metadata]
# replace with your username: # replace with your username:
name = guan name = guan
version = 0.0.42 version = 0.0.43
author = guanjihuan author = guanjihuan
author_email = guanjihuan@163.com author_email = guanjihuan@163.com
description = An open source python package description = An open source python package

7
PyPI/src/guan/Hamiltonian_of_finite_size_systems.py
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@@ -3,6 +3,7 @@
# Hamiltonian of finite size systems # Hamiltonian of finite size systems
import numpy as np import numpy as np
import guan
def finite_size_along_one_direction(N, on_site=0, hopping=1, period=0): def finite_size_along_one_direction(N, on_site=0, hopping=1, period=0):
on_site = np.array(on_site) on_site = np.array(on_site)
@@ -106,9 +107,9 @@ def hopping_along_zigzag_direction_for_graphene(N):
return hopping return hopping
def finite_size_along_two_directions_for_graphene(N1, N2, period_1=0, period_2=0): def finite_size_along_two_directions_for_graphene(N1, N2, period_1=0, period_2=0):
on_site = finite_size_along_one_direction(4) on_site = guan.finite_size_along_one_direction(4)
hopping_1 = hopping_along_zigzag_direction_for_graphene(1) hopping_1 = guan.hopping_along_zigzag_direction_for_graphene(1)
hopping_2 = np.zeros((4, 4), dtype=complex) hopping_2 = np.zeros((4, 4), dtype=complex)
hopping_2[3, 0] = 1 hopping_2[3, 0] = 1
hamiltonian = finite_size_along_two_directions_for_square_lattice(N1, N2, on_site, hopping_1, hopping_2, period_1, period_2) hamiltonian = guan.finite_size_along_two_directions_for_square_lattice(N1, N2, on_site, hopping_1, hopping_2, period_1, period_2)
return hamiltonian return hamiltonian

39
PyPI/src/guan/calculate_topological_invariant.py
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@@ -38,6 +38,45 @@ def calculate_chern_number_for_square_lattice(hamiltonian_function, precision=10
chern_number = chern_number/(2*pi*1j) chern_number = chern_number/(2*pi*1j)
return chern_number return chern_number
def calculate_chern_number_for_square_lattice_with_Wilson_loop(hamiltonian_function, precision_of_plaquettes=10, precision_of_Wilson_loop=100):
delta = 2*pi/precision_of_plaquettes
chern_number = 0
for kx in np.arange(-pi, pi, delta):
for ky in np.arange(-pi, pi, delta):
vector_array = []
# line_1
for i0 in range(precision_of_Wilson_loop+1):
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+1))
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+1), 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-1):
H_delta = hamiltonian_function(kx, ky+delta-delta/precision_of_Wilson_loop*(i0+1))
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])
arg = np.log(np.diagonal(Wilson_loop))/1j
chern_number = chern_number + arg
chern_number = chern_number/(2*pi)
return chern_number
def calculate_chern_number_for_honeycomb_lattice(hamiltonian_function, a=1, precision=300): def calculate_chern_number_for_honeycomb_lattice(hamiltonian_function, a=1, precision=300):
if np.array(hamiltonian_function(0, 0)).shape==(): if np.array(hamiltonian_function(0, 0)).shape==():
dim = 1 dim = 1