r"""
This module contains two equivalent functions that create an instance of the `Haldane
model <https://doi.org/10.1103/PhysRevLett.61.2015>`_ with PythTB or TBmodels. The Haldane
model is a tight-binding model describing spinless electrons hopping on a 2D honeycomb
lattice with a staggered magnetic flux. The parameters of the model are the nearest-neighbor
hopping :math:`t`, the on-site energy term :math:`\pm\Delta` with opposite signs on the two
sublattices and the second-nearest-neighbor hopping term :math:`t_2e^{i\phi}`. The
Hamiltonian of the model reads:
.. math::
\mathcal{H} = \Delta\sum_{i}\left( c_{i,A}^{\dagger}c_{i,A}-c_{i,B}^{\dagger}c_{i,B} \right) +
t \sum_{\langle ij\rangle}c_i^{\dagger}c_j+t_2\sum_{\langle\langle ij\rangle\rangle}
e^{i\nu_{ij}\phi}c_i^{\dagger}c_j + \mathrm{h.c.}
where :math:`\nu_{ij}=\pm 1` is a factor accounting for the direction of the complex hopping.
"""
import pythtb
from tbmodels import Model
import numpy as np
[docs]
def haldane_pythtb(delta, t, t2, phi, ptb_version=pythtb.__version__):
r"""
The Haldane model with PythTB.
"""
# From http://www.physics.rutgers.edu/pythtb/examples.html#haldane-model
lat_cell = [[1.0, 0.0], [0.5, np.sqrt(3.0) / 2.0]]
orb = [[0.0, 0.0], [1.0 / 3.0, 1.0 / 3.0]]
if ptb_version < "2.0.0":
model = pythtb.tb_model(2, 2, lat_cell, orb)
else:
lat = pythtb.Lattice(lat_cell, orb, periodic_dirs=[0, 1])
model = pythtb.TBModel(lattice=lat, spinful=False)
model.set_onsite([-delta, delta])
for lvec in ([0, 0], [-1, 0], [0, -1]):
model.set_hop(t, 0, 1, lvec)
for lvec in ([1, 0], [-1, 1], [0, -1]):
model.set_hop(t2 * np.exp(1.0j * phi), 0, 0, lvec)
for lvec in ([-1, 0], [1, -1], [0, 1]):
model.set_hop(t2 * np.exp(1.0j * phi), 1, 1, lvec)
return model
[docs]
def haldane_tbmodels(delta, t, t2, phi):
r"""
The Haldane model with TBmodels.
"""
primitive_cell = [[1.0, 0.0], [0.5, np.sqrt(3.0) / 2.0]]
orb = [[0.0, 0.0], [1.0 / 3.0, 1.0 / 3.0]]
h_model = Model(on_site=[-delta, delta], dim=2, occ=1, pos=orb, uc=primitive_cell)
for lvec in ([0, 0], [-1, 0], [0, -1]):
h_model.add_hop(t, 0, 1, lvec)
for lvec in ([1, 0], [-1, 1], [0, -1]):
h_model.add_hop(t2 * np.exp(1.0j * phi), 0, 0, lvec)
for lvec in ([-1, 0], [1, -1], [0, 1]):
h_model.add_hop(t2 * np.exp(1.0j * phi), 1, 1, lvec)
return h_model
