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guanjihuan
2023-11-07 03:38:46 +08:00
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2021.12.09_nested_Wilson_loop_of_BBH_model/BBH_bands.py Normal file
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"""
This code is supported by the website: https://www.guanjihuan.com
The newest version of this code is on the web page: https://www.guanjihuan.com/archives/17984
"""
import numpy as np
import cmath
from math import *
import functools
def hamiltonian(kx, ky): # BBH model
# label of atoms in a unit cell
# (2) —— (0)
# | |
# (1) —— (3)
gamma_x = 0.5 # hopping inside one unit cell
lambda_x = 1 # hopping between unit cells
gamma_y = gamma_x
lambda_y = lambda_x
h = np.zeros((4, 4), dtype=complex)
h[0, 2] = gamma_x+lambda_x*cmath.exp(1j*kx)
h[1, 3] = gamma_x+lambda_x*cmath.exp(-1j*kx)
h[0, 3] = gamma_y+lambda_y*cmath.exp(1j*ky)
h[1, 2] = -gamma_y-lambda_y*cmath.exp(-1j*ky)
h[2, 0] = np.conj(h[0, 2])
h[3, 1] = np.conj(h[1, 3])
h[3, 0] = np.conj(h[0, 3])
h[2, 1] = np.conj(h[1, 2])
return h
def main():
kx = np.arange(-pi, pi, 0.05)
ky = np.arange(-pi, pi, 0.05)
eigenvalue_array = calculate_eigenvalue_with_two_parameters(kx, ky, hamiltonian)
plot_3d_surface(kx, ky, eigenvalue_array, xlabel='kx', ylabel='ky', zlabel='E', title='BBH bands')
hamiltonian0 = functools.partial(hamiltonian, ky=0)
eigenvalue_array = calculate_eigenvalue_with_one_parameter(kx, hamiltonian0)
plot(kx, eigenvalue_array, xlabel='kx', ylabel='E', title='BBH bands ky=0')
# import guan
# eigenvalue_array = guan.calculate_eigenvalue_with_two_parameters(kx, ky, hamiltonian)
# guan.plot_3d_surface(kx, ky, eigenvalue_array, xlabel='kx', ylabel='ky', zlabel='E', title='BBH bands')
# hamiltonian0 = functools.partial(hamiltonian, ky=0)
# eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(kx, hamiltonian0)
# guan.plot(kx, eigenvalue_array, xlabel='kx', ylabel='E', title='BBH bands ky=0')
def calculate_eigenvalue_with_one_parameter(x_array, hamiltonian_function, print_show=0):
dim_x = np.array(x_array).shape[0]
i0 = 0
if np.array(hamiltonian_function(0)).shape==():
eigenvalue_array = np.zeros((dim_x, 1))
for x0 in x_array:
hamiltonian = hamiltonian_function(x0)
eigenvalue_array[i0, 0] = np.real(hamiltonian)
i0 += 1
else:
dim = np.array(hamiltonian_function(0)).shape[0]
eigenvalue_array = np.zeros((dim_x, dim))
for x0 in x_array:
if print_show==1:
print(x0)
hamiltonian = hamiltonian_function(x0)
eigenvalue, eigenvector = np.linalg.eigh(hamiltonian)
eigenvalue_array[i0, :] = eigenvalue
i0 += 1
return eigenvalue_array
def calculate_eigenvalue_with_two_parameters(x_array, y_array, hamiltonian_function, print_show=0, print_show_more=0):
dim_x = np.array(x_array).shape[0]
dim_y = np.array(y_array).shape[0]
if np.array(hamiltonian_function(0,0)).shape==():
eigenvalue_array = np.zeros((dim_y, dim_x, 1))
i0 = 0
for y0 in y_array:
j0 = 0
for x0 in x_array:
hamiltonian = hamiltonian_function(x0, y0)
eigenvalue_array[i0, j0, 0] = np.real(hamiltonian)
j0 += 1
i0 += 1
else:
dim = np.array(hamiltonian_function(0, 0)).shape[0]
eigenvalue_array = np.zeros((dim_y, dim_x, dim))
i0 = 0
for y0 in y_array:
j0 = 0
if print_show==1:
print(y0)
for x0 in x_array:
if print_show_more==1:
print(x0)
hamiltonian = hamiltonian_function(x0, y0)
eigenvalue, eigenvector = np.linalg.eigh(hamiltonian)
eigenvalue_array[i0, j0, :] = eigenvalue
j0 += 1
i0 += 1
return eigenvalue_array
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 matplotlib.pyplot as plt
fig, ax = plt.subplots()
plt.subplots_adjust(bottom=adjust_bottom, left=adjust_left)
ax.plot(x_array, y_array, style, linewidth=linewidth, markersize=markersize)
ax.grid()
ax.set_title(title, fontsize=fontsize, fontfamily='Times New Roman')
ax.set_xlabel(xlabel, fontsize=fontsize, fontfamily='Times New Roman')
ax.set_ylabel(ylabel, fontsize=fontsize, fontfamily='Times New Roman')
if y_min!=None or y_max!=None:
if y_min==None:
y_min=min(y_array)
if y_max==None:
y_max=max(y_array)
ax.set_ylim(y_min, y_max)
ax.tick_params(labelsize=labelsize)
labels = ax.get_xticklabels() + ax.get_yticklabels()
[label.set_fontname('Times New Roman') for label in labels]
if save == 1:
plt.savefig(filename+file_format, dpi=dpi)
if show == 1:
plt.show()
plt.close('all')
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 matplotlib.pyplot as plt
from matplotlib import cm
from matplotlib.ticker import LinearLocator
matrix = np.array(matrix)
fig, ax = plt.subplots(subplot_kw={"projection": "3d"})
plt.subplots_adjust(bottom=0.1, right=0.65)
x_array, y_array = np.meshgrid(x_array, y_array)
if len(matrix.shape) == 2:
surf = ax.plot_surface(x_array, y_array, matrix, rcount=rcount, ccount=ccount, cmap=cm.coolwarm, linewidth=0, antialiased=False)
elif len(matrix.shape) == 3:
for i0 in range(matrix.shape[2]):
surf = ax.plot_surface(x_array, y_array, matrix[:,:,i0], rcount=rcount, ccount=ccount, cmap=cm.coolwarm, linewidth=0, antialiased=False)
ax.set_title(title, fontsize=fontsize, fontfamily='Times New Roman')
ax.set_xlabel(xlabel, fontsize=fontsize, fontfamily='Times New Roman')
ax.set_ylabel(ylabel, fontsize=fontsize, fontfamily='Times New Roman')
ax.set_zlabel(zlabel, fontsize=fontsize, fontfamily='Times New Roman')
ax.zaxis.set_major_locator(LinearLocator(5))
ax.zaxis.set_major_formatter('{x:.2f}')
if z_min!=None or z_max!=None:
if z_min==None:
z_min=matrix.min()
if z_max==None:
z_max=matrix.max()
ax.set_zlim(z_min, z_max)
ax.tick_params(labelsize=labelsize)
labels = ax.get_xticklabels() + ax.get_yticklabels() + ax.get_zticklabels()
[label.set_fontname('Times New Roman') for label in labels]
cax = plt.axes([0.8, 0.1, 0.05, 0.8])
cbar = fig.colorbar(surf, cax=cax)
cbar.ax.tick_params(labelsize=labelsize)
for l in cbar.ax.yaxis.get_ticklabels():
l.set_family('Times New Roman')
if save == 1:
plt.savefig(filename+file_format, dpi=dpi)
if show == 1:
plt.show()
plt.close('all')
if __name__ == '__main__':
main()