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guanjihuan 2022-06-15 15:02:17 +08:00
parent 02976831bb
commit 23be72b2c1
4 changed files with 28 additions and 17 deletions
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2
academic_codes/2019.10.24_Halmiltonian_and_bands_of_Haldane_model/2D_Haldane_model.py
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@ -25,7 +25,7 @@ def hamiltonian(k1, k2, M, t1, t2, phi, a=1/sqrt(3)): # Haldane哈密顿量(a
h1[0, 1] = h1[1, 0].conj() h1[0, 1] = h1[1, 0].conj()
# 最近邻项也可写成这种形式 # 最近邻项也可写成这种形式
# h1[1, 0] = t1+t1*cmath.exp(1j*sqrt(3)/2*k1*a-1j*3/2*k2*a)-t1*cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a) # h1[1, 0] = t1+t1*cmath.exp(1j*sqrt(3)/2*k1*a-1j*3/2*k2*a)+t1*cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a)
# h1[0, 1] = h1[1, 0].conj() # h1[0, 1] = h1[1, 0].conj()
# 次近邻项 # 次近邻项

15
academic_codes/2020.07.13_calculation_of_Chern_number_in_Haldane_model/Chern_number_in_Haldane_model.py
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@ -4,18 +4,17 @@ The newest version of this code is on the web page: https://www.guanjihuan.com/a
""" """
import numpy as np import numpy as np
import matplotlib.pyplot as plt
from math import * # 引入pi, cos等 from math import * # 引入pi, cos等
import cmath import cmath
import time import time
import functools # 使用偏函数functools.partial() import functools # 使用偏函数functools.partial()
def hamiltonian(k1, k2, M, t1, t2, phi, a=1/sqrt(3)): # Haldane哈密顿量(a为原子间距，不赋值的话默认为1/sqrt(3)） def hamiltonian(k1, k2, M, t1, t2, phi, a=1/sqrt(3)): # Haldane哈密顿量（a为原子间距，不赋值的话默认为1/sqrt(3)）
# 初始化为零矩阵 # 初始化为零矩阵
h0 = np.zeros((2, 2))*(1+0j) # 乘(1+0j)是为了把h0转为复数 h0 = np.zeros((2, 2), dtype=complex)
h1 = np.zeros((2, 2))*(1+0j) h1 = np.zeros((2, 2), dtype=complex)
h2 = np.zeros((2, 2))*(1+0j) h2 = np.zeros((2, 2), dtype=complex)
# 质量项(mass term), 用于打开带隙 # 质量项(mass term), 用于打开带隙
h0[0, 0] = M h0[0, 0] = M
@ -25,6 +24,10 @@ def hamiltonian(k1, k2, M, t1, t2, phi, a=1/sqrt(3)): # Haldane哈密顿量(a
h1[1, 0] = t1*(cmath.exp(1j*k2*a)+cmath.exp(1j*sqrt(3)/2*k1*a-1j/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j/2*k2*a)) h1[1, 0] = t1*(cmath.exp(1j*k2*a)+cmath.exp(1j*sqrt(3)/2*k1*a-1j/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j/2*k2*a))
h1[0, 1] = h1[1, 0].conj() h1[0, 1] = h1[1, 0].conj()
# # 最近邻项也可写成这种形式
# h1[1, 0] = t1+t1*cmath.exp(1j*sqrt(3)/2*k1*a-1j*3/2*k2*a)+t1*cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a)
# h1[0, 1] = h1[1, 0].conj()
#次近邻项 # 对应陈数为-1 #次近邻项 # 对应陈数为-1
h2[0, 0] = t2*cmath.exp(-1j*phi)*(cmath.exp(1j*sqrt(3)*k1*a)+cmath.exp(-1j*sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a)) h2[0, 0] = t2*cmath.exp(-1j*phi)*(cmath.exp(1j*sqrt(3)*k1*a)+cmath.exp(-1j*sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a))
h2[1, 1] = t2*cmath.exp(1j*phi)*(cmath.exp(1j*sqrt(3)*k1*a)+cmath.exp(-1j*sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a)) h2[1, 1] = t2*cmath.exp(1j*phi)*(cmath.exp(1j*sqrt(3)*k1*a)+cmath.exp(-1j*sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a))
@ -88,4 +91,4 @@ def main():
if __name__ == '__main__': if __name__ == '__main__':
main() main()

14
academic_codes/2020.07.13_calculation_of_Chern_number_in_Haldane_model/Chern_number_in_Haldane_model_by_integration_method_2.py
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@ -11,11 +11,11 @@ import time
import functools # 使用偏函数functools.partial() import functools # 使用偏函数functools.partial()
def hamiltonian(k1, k2, M, t1, t2, phi, a=1/sqrt(3)): # Haldane哈密顿量(a为原子间距，不赋值的话默认为1/sqrt(3)） def hamiltonian(k1, k2, M, t1, t2, phi, a=1/sqrt(3)): # Haldane哈密顿量（a为原子间距，不赋值的话默认为1/sqrt(3)）
# 初始化为零矩阵 # 初始化为零矩阵
h0 = np.zeros((2, 2))*(1+0j) # 乘(1+0j)是为了把h0转为复数 h0 = np.zeros((2, 2), dtype=complex)
h1 = np.zeros((2, 2))*(1+0j) h1 = np.zeros((2, 2), dtype=complex)
h2 = np.zeros((2, 2))*(1+0j) h2 = np.zeros((2, 2), dtype=complex)
# 质量项(mass term), 用于打开带隙 # 质量项(mass term), 用于打开带隙
h0[0, 0] = M h0[0, 0] = M
@ -25,6 +25,10 @@ def hamiltonian(k1, k2, M, t1, t2, phi, a=1/sqrt(3)): # Haldane哈密顿量(a
h1[1, 0] = t1*(cmath.exp(1j*k2*a)+cmath.exp(1j*sqrt(3)/2*k1*a-1j/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j/2*k2*a)) h1[1, 0] = t1*(cmath.exp(1j*k2*a)+cmath.exp(1j*sqrt(3)/2*k1*a-1j/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j/2*k2*a))
h1[0, 1] = h1[1, 0].conj() h1[0, 1] = h1[1, 0].conj()
# # 最近邻项也可写成这种形式
# h1[1, 0] = t1+t1*cmath.exp(1j*sqrt(3)/2*k1*a-1j*3/2*k2*a)+t1*cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a)
# h1[0, 1] = h1[1, 0].conj()
#次近邻项 # 对应陈数为-1 #次近邻项 # 对应陈数为-1
h2[0, 0] = t2*cmath.exp(-1j*phi)*(cmath.exp(1j*sqrt(3)*k1*a)+cmath.exp(-1j*sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a)) h2[0, 0] = t2*cmath.exp(-1j*phi)*(cmath.exp(1j*sqrt(3)*k1*a)+cmath.exp(-1j*sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a))
h2[1, 1] = t2*cmath.exp(1j*phi)*(cmath.exp(1j*sqrt(3)*k1*a)+cmath.exp(-1j*sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a)) h2[1, 1] = t2*cmath.exp(1j*phi)*(cmath.exp(1j*sqrt(3)*k1*a)+cmath.exp(-1j*sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a))
@ -84,4 +88,4 @@ def main():
if __name__ == '__main__': if __name__ == '__main__':
main() main()

14
academic_codes/2020.07.13_calculation_of_Chern_number_in_Haldane_model/Chern_number_in_Haldane_model_by_integration_method_3.py
View File

@ -11,11 +11,11 @@ import time
import functools # 使用偏函数functools.partial() import functools # 使用偏函数functools.partial()
def hamiltonian(k1, k2, M, t1, t2, phi, a=1/sqrt(3)): # Haldane哈密顿量(a为原子间距，不赋值的话默认为1/sqrt(3)） def hamiltonian(k1, k2, M, t1, t2, phi, a=1/sqrt(3)): # Haldane哈密顿量# Haldane哈密顿量（a为原子间距，不赋值的话默认为1/sqrt(3)）
# 初始化为零矩阵 # 初始化为零矩阵
h0 = np.zeros((2, 2))*(1+0j) # 乘(1+0j)是为了把h0转为复数 h0 = np.zeros((2, 2), dtype=complex)
h1 = np.zeros((2, 2))*(1+0j) h1 = np.zeros((2, 2), dtype=complex)
h2 = np.zeros((2, 2))*(1+0j) h2 = np.zeros((2, 2), dtype=complex)
# 质量项(mass term), 用于打开带隙 # 质量项(mass term), 用于打开带隙
h0[0, 0] = M h0[0, 0] = M
@ -25,6 +25,10 @@ def hamiltonian(k1, k2, M, t1, t2, phi, a=1/sqrt(3)): # Haldane哈密顿量(a
h1[1, 0] = t1*(cmath.exp(1j*k2*a)+cmath.exp(1j*sqrt(3)/2*k1*a-1j/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j/2*k2*a)) h1[1, 0] = t1*(cmath.exp(1j*k2*a)+cmath.exp(1j*sqrt(3)/2*k1*a-1j/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j/2*k2*a))
h1[0, 1] = h1[1, 0].conj() h1[0, 1] = h1[1, 0].conj()
# # 最近邻项也可写成这种形式
# h1[1, 0] = t1+t1*cmath.exp(1j*sqrt(3)/2*k1*a-1j*3/2*k2*a)+t1*cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a)
# h1[0, 1] = h1[1, 0].conj()
#次近邻项 # 对应陈数为-1 #次近邻项 # 对应陈数为-1
h2[0, 0] = t2*cmath.exp(-1j*phi)*(cmath.exp(1j*sqrt(3)*k1*a)+cmath.exp(-1j*sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a)) h2[0, 0] = t2*cmath.exp(-1j*phi)*(cmath.exp(1j*sqrt(3)*k1*a)+cmath.exp(-1j*sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a))
h2[1, 1] = t2*cmath.exp(1j*phi)*(cmath.exp(1j*sqrt(3)*k1*a)+cmath.exp(-1j*sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a)) h2[1, 1] = t2*cmath.exp(1j*phi)*(cmath.exp(1j*sqrt(3)*k1*a)+cmath.exp(-1j*sqrt(3)/2*k1*a+1j*3/2*k2*a)+cmath.exp(-1j*sqrt(3)/2*k1*a-1j*3/2*k2*a))
@ -92,4 +96,4 @@ def main():
if __name__ == '__main__': if __name__ == '__main__':
main() main()