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guanjihuan
2023-07-26 00:46:01 +08:00
parent c7cbcd09af
commit 822fa7e626
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50
academic_codes/Landau_levels/2021.01.07_Hofstadter_butterfly_in_square_lattice/Hofstadter_butterfly_in_square_lattice.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/8491
"""
import numpy as np
import cmath
import matplotlib.pyplot as plt
def main():
for n in np.arange(1, 11):
print('n=', n)
width = n
length = n
B_array = np.arange(0, 1, 0.001)
eigenvalue_all = np.zeros((B_array.shape[0], width*length))
i0 = 0
for B in B_array:
# print(B)
h = hamiltonian(width, length, B)
eigenvalue, eigenvector = np.linalg.eig(h)
eigenvalue_all[i0, :] = np.real(eigenvalue)
i0 += 1
plt.plot(B_array, eigenvalue_all, '.r', markersize=0.5)
plt.title('width=length='+str(n))
plt.xlabel('B*a^2/phi_0')
plt.ylabel('E')
plt.savefig('width=length='+str(n)+'.jpg', dpi=300)
plt.close('all') # 关闭所有plt，防止循环画图时占用内存
# plt.show()
def hamiltonian(width, length, B): # 方格子哈密顿量
h = np.zeros((width*length, width*length), dtype=complex)
# y方向的跃迁
for x in range(length):
for y in range(width-1):
h[x*width+y, x*width+y+1] = 1
h[x*width+y+1, x*width+y] = 1
# x方向的跃迁
for x in range(length-1):
for y in range(width):
h[x*width+y, (x+1)*width+y] = 1*cmath.exp(-2*np.pi*1j*B*y)
h[(x+1)*width+y, x*width+y] = 1*cmath.exp(2*np.pi*1j*B*y)
return h
if __name__ == "__main__":
main()

99
academic_codes/Landau_levels/2021.04.24_Hofstadter_butterfly_of_graphene_ribbon/Hofstadter_butterfly_of_graphene_ribbon.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/12185
"""
import numpy as np
from math import *
import cmath
import functools
def hamiltonian(B, k, N, M, t1, a): # graphene哈密顿量（N是条带的宽度参数）
# 初始化为零矩阵
h00 = np.zeros((4*N, 4*N), dtype=complex)
h01 = np.zeros((4*N, 4*N), dtype=complex)
# 原胞内的跃迁h00
for i in range(N):
h00[i*4+0, i*4+0] = M
h00[i*4+1, i*4+1] = -M
h00[i*4+2, i*4+2] = M
h00[i*4+3, i*4+3] = -M
# 最近邻
h00[i*4+0, i*4+1] = t1*cmath.exp(-2*pi*1j*B*(3*a*i+1/4*a)*(np.sqrt(3)/2*a))
h00[i*4+1, i*4+0] = np.conj(h00[i*4+0, i*4+1])
h00[i*4+1, i*4+2] = t1
h00[i*4+2, i*4+1] = np.conj(h00[i*4+1, i*4+2])
h00[i*4+2, i*4+3] = t1*cmath.exp(2*pi*1j*B*(3*a*i+7/4*a)*(np.sqrt(3)/2)*a)
h00[i*4+3, i*4+2] = np.conj(h00[i*4+2, i*4+3])
for i in range(N-1):
# 最近邻
h00[i*4+3, (i+1)*4+0] = t1
h00[(i+1)*4+0, i*4+3] = t1
# 原胞间的跃迁h01
for i in range(N):
# 最近邻
h01[i*4+1, i*4+0] = t1*cmath.exp(-2*pi*1j*B*(3*a*i+1/4*a)*(np.sqrt(3)/2*a))
h01[i*4+2, i*4+3] = t1*cmath.exp(-2*pi*1j*B*(3*a*i+7/4*a)*(np.sqrt(3)/2*a))
matrix = h00 + h01*cmath.exp(1j*k) + h01.transpose().conj()*cmath.exp(-1j*k)
return matrix
def main():
N = 30
a = 1
hamiltonian_function0 = functools.partial(hamiltonian, k=0, N=N, M=0, t1=1, a=a)
B_array = np.linspace(0, 1/(3*np.sqrt(3)/2*a*a), 100)
BS_array = B_array*(3*np.sqrt(3)/2*a*a)
eigenvalue_array = calculate_eigenvalue_with_one_parameter(B_array, hamiltonian_function0)
plot(BS_array, eigenvalue_array, xlabel='Flux (BS/phi_0)', ylabel='E', title='Ny=%i'%N, filename='a', show=1, save=0, style='k.', y_min=None, y_max=None, markersize=3)
# import guan
# eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(B_array, hamiltonian_function0)
# guan.plot(BS_array, eigenvalue_array, xlabel='Flux (BS/phi_0)', ylabel='E', title='Ny=%i'%N, filename='a', show=1, save=0, style='k.', y_min=None, y_max=None, markersize=3)
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 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')
if __name__ == '__main__':
main()

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academic_codes/Landau_levels/2022.08.03_Landau_levels_of_honeycomb_lattice/Landau_levels_of_honeycomb_lattice.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/23834
"""
import numpy as np
from math import *
import cmath
import functools
def hamiltonian(kx, ky, B, N, M, t1, a): # 在磁场下的二维石墨烯，取磁元胞
h00 = np.zeros((4*N, 4*N), dtype=complex)
h01 = np.zeros((4*N, 4*N), dtype=complex)
# 原胞内的跃迁h00
for i in range(N):
h00[i*4+0, i*4+0] = M
h00[i*4+1, i*4+1] = -M
h00[i*4+2, i*4+2] = M
h00[i*4+3, i*4+3] = -M
# 最近邻
h00[i*4+0, i*4+1] = t1*cmath.exp(-2*pi*1j*B*(3*a*i+1/4*a)*(np.sqrt(3)/2*a))
h00[i*4+1, i*4+0] = np.conj(h00[i*4+0, i*4+1])
h00[i*4+1, i*4+2] = t1
h00[i*4+2, i*4+1] = np.conj(h00[i*4+1, i*4+2])
h00[i*4+2, i*4+3] = t1*cmath.exp(2*pi*1j*B*(3*a*i+7/4*a)*(np.sqrt(3)/2)*a)
h00[i*4+3, i*4+2] = np.conj(h00[i*4+2, i*4+3])
for i in range(N-1):
# 最近邻
h00[i*4+3, (i+1)*4+0] = t1
h00[(i+1)*4+0, i*4+3] = t1
h00[4*(N-1)+3, 0] = t1*cmath.exp(1j*ky)
h00[0, 4*(N-1)+3] = t1*cmath.exp(-1j*ky)
# 原胞间的跃迁h01
for i in range(N):
# 最近邻
h01[i*4+1, i*4+0] = t1*cmath.exp(-2*pi*1j*B*(3*a*i+1/4*a)*(np.sqrt(3)/2*a))
h01[i*4+2, i*4+3] = t1*cmath.exp(-2*pi*1j*B*(3*a*i+7/4*a)*(np.sqrt(3)/2*a))
matrix = h00 + h01*cmath.exp(1j*kx) + h01.transpose().conj()*cmath.exp(-1j*kx)
return matrix
def main():
N = 300
a = 1
hamiltonian_function = functools.partial(hamiltonian, ky=0, B=1/(3*np.sqrt(3)/2*a*a*N), N=N, M=0, t1=1, a=a)
# 查看能带图
k_array = np.linspace(-pi, pi, 10)
eigenvalue_array = calculate_eigenvalue_with_one_parameter(k_array, hamiltonian_function)
plot(k_array, eigenvalue_array, xlabel='kx', ylabel='E', title='ky=0 N=%i Φ/Φ_0=1/(3*np.sqrt(3)/2*a*a*N)'%N, style='k-', y_max=1, y_min=-1)
# import guan
# k_array = np.linspace(-pi, pi, 10)
# eigenvalue_array = guan.calculate_eigenvalue_with_one_parameter(k_array, hamiltonian_function)
# guan.plot(k_array, eigenvalue_array, xlabel='kx', ylabel='E', title='ky=0 N=%i Φ/Φ_0=1/(3*np.sqrt(3)/2*a*a*N)'%N, style='k-', y_max=1, y_min=-1)
# 查看关系
eigenvalue, eigenvector = np.linalg.eigh(hamiltonian_function(0))
print('本征值个数：', eigenvalue.shape)
new_eigenvalue = []
for eigen in eigenvalue:
if -0.1<eigen<0.8: # 找某个范围内的本征值
if new_eigenvalue == []:
new_eigenvalue.append(eigen)
else:
if np.abs(eigen-new_eigenvalue[-1])>0.001: # 去除简并
new_eigenvalue.append(eigen)
print('大于等于0的本征值个数：', len(new_eigenvalue), '\n')
print(new_eigenvalue)
plot(range(len(new_eigenvalue)), np.square(np.real(new_eigenvalue)), xlabel='n', ylabel='E^2', style='o-')
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 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.grid()
ax.tick_params(labelsize=labelsize)
labels = ax.get_xticklabels() + ax.get_yticklabels()
[label.set_fontname('Times New Roman') for label in labels]
ax.plot(x_array, y_array, style, linewidth=linewidth, markersize=markersize)
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)
if save == 1:
plt.savefig(filename+file_format, dpi=dpi)
if show == 1:
plt.show()
plt.close('all')
if __name__ == '__main__':
main()