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guanjihuan
2021-12-30 03:59:52 +08:00
parent 3d98ec8cdd
commit 518d0ad09f
3 changed files with 38 additions and 1 deletions
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PyPI/src/guan/calculate_topological_invariant.py
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@@ -38,6 +38,42 @@ def calculate_chern_number_for_square_lattice(hamiltonian_function, precision=10
chern_number = chern_number/(2*pi*1j)
return chern_number
def calculate_chern_number_for_honeycomb_lattice(hamiltonian_function, a=1, precision=300):
if np.array(hamiltonian_function(0, 0)).shape==():
dim = 1
else:
dim = np.array(hamiltonian_function(0, 0)).shape[0]
chern_number = np.zeros(dim, dtype=complex)
L1 = 4*sqrt(3)*pi/9/a
L2 = 2*sqrt(3)*pi/9/a
L3 = 2*pi/3/a
delta1 = 2*L1/precision
delta3 = 2*L3/precision
for kx in np.arange(-L1, L1, delta1):
for ky in np.arange(-L3, L3, delta3):
if (-L2<=kx<=L2) or (kx>L2 and -(L1-kx)*tan(pi/3)<=ky<=(L1-kx)*tan(pi/3)) or (kx<-L2 and -(kx-(-L1))*tan(pi/3)<=ky<=(kx-(-L1))*tan(pi/3)):
H = hamiltonian_function(kx, ky)
vector = guan.calculate_eigenvector(H)
H_delta_kx = hamiltonian_function(kx+delta1, ky)
vector_delta_kx = guan.calculate_eigenvector(H_delta_kx)
H_delta_ky = hamiltonian_function(kx, ky+delta3)
vector_delta_ky = guan.calculate_eigenvector(H_delta_ky)
H_delta_kx_ky = hamiltonian_function(kx+delta1, ky+delta3)
vector_delta_kx_ky = guan.calculate_eigenvector(H_delta_kx_ky)
for i in range(dim):
vector_i = vector[:, i]
vector_delta_kx_i = vector_delta_kx[:, i]
vector_delta_ky_i = vector_delta_ky[:, i]
vector_delta_kx_ky_i = vector_delta_kx_ky[:, i]
Ux = np.dot(np.conj(vector_i), vector_delta_kx_i)/abs(np.dot(np.conj(vector_i), vector_delta_kx_i))
Uy = np.dot(np.conj(vector_i), vector_delta_ky_i)/abs(np.dot(np.conj(vector_i), vector_delta_ky_i))
Ux_y = np.dot(np.conj(vector_delta_ky_i), vector_delta_kx_ky_i)/abs(np.dot(np.conj(vector_delta_ky_i), vector_delta_kx_ky_i))
Uy_x = np.dot(np.conj(vector_delta_kx_i), vector_delta_kx_ky_i)/abs(np.dot(np.conj(vector_delta_kx_i), vector_delta_kx_ky_i))
F = cmath.log(Ux*Uy_x*(1/Ux_y)*(1/Uy))
chern_number[i] = chern_number[i] + F
chern_number = chern_number/(2*pi*1j)
return chern_number
def calculate_wilson_loop(hamiltonian_function, k_min=-pi, k_max=pi, precision=100):
k_array = np.linspace(k_min, k_max, precision)
dim = np.array(hamiltonian_function(0)).shape[0]