"""Prototypical example of a quantum model: the transverse field Ising model.
Like the :class:`~tenpy.models.xxz_chain.XXZChain`, the transverse field ising chain
:class:`TFIChain` is contained in the more general :class:`~tenpy.models.spins.SpinChain`;
the idea is more to serve as a pedagogical example for a 'model'.
We choose the field along z to allow to conserve the parity, if desired.
"""
# Copyright 2018-2019 TeNPy Developers, GNU GPLv3
from .model import CouplingMPOModel, NearestNeighborModel
from ..tools.params import get_parameter
from ..networks.site import SpinHalfSite
__all__ = ['TFIModel', 'TFIChain']
[docs]class TFIModel(CouplingMPOModel):
r"""Transverse field Ising model on a general lattice.
The Hamiltonian reads:
.. math ::
H = - \sum_{\langle i,j\rangle, i < j} \mathtt{J} \sigma^x_i \sigma^x_{j}
- \sum_{i} \mathtt{g} \sigma^z_i
Here, :math:`\langle i,j \rangle, i< j` denotes nearest neighbor pairs, each pair appearing
exactly once.
All parameters are collected in a single dictionary `model_params` and read out with
:func:`~tenpy.tools.params.get_parameter`.
Parameters
----------
conserve : None | 'parity'
What should be conserved. See :class:`~tenpy.networks.Site.SpinHalfSite`.
J, g : float | array
Couplings as defined for the Hamiltonian above.
lattice : str | :class:`~tenpy.models.lattice.Lattice`
Instance of a lattice class for the underlaying geometry.
Alternatively a string being the name of one of the Lattices defined in
:mod:`~tenpy.models.lattice`, e.g. ``"Chain", "Square", "HoneyComb", ...``.
bc_MPS : {'finite' | 'infinte'}
MPS boundary conditions along the x-direction.
For 'infinite' boundary conditions, repeat the unit cell in x-direction.
Coupling boundary conditions in x-direction are chosen accordingly.
Only used if `lattice` is a string.
order : string
Ordering of the sites in the MPS, e.g. 'default', 'snake';
see :meth:`~tenpy.models.lattice.Lattice.ordering`.
Only used if `lattice` is a string.
L : int
Lenght of the lattice.
Only used if `lattice` is the name of a 1D Lattice.
Lx, Ly : int
Length of the lattice in x- and y-direction.
Only used if `lattice` is the name of a 2D Lattice.
bc_y : 'ladder' | 'cylinder'
Boundary conditions in y-direction.
Only used if `lattice` is the name of a 2D Lattice.
"""
def __init__(self, model_params):
CouplingMPOModel.__init__(self, model_params)
[docs] def init_sites(self, model_params):
conserve = get_parameter(model_params, 'conserve', 'parity', self.name)
assert conserve != 'Sz'
if conserve == 'best':
conserve = 'parity'
if self.verbose >= 1.:
print(self.name + ": set conserve to", conserve)
site = SpinHalfSite(conserve=conserve)
return site
[docs] def init_terms(self, model_params):
J = get_parameter(model_params, 'J', 1., self.name, True)
g = get_parameter(model_params, 'g', 1., self.name, True)
for u in range(len(self.lat.unit_cell)):
self.add_onsite(-g, u, 'Sigmaz')
for u1, u2, dx in self.lat.pairs['nearest_neighbors']:
self.add_coupling(-J, u1, 'Sigmax', u2, 'Sigmax', dx)
# done
[docs]class TFIChain(TFIModel, NearestNeighborModel):
"""The :class:`TFIModel` on a Chain, suitable for TEBD.
See the :class:`TFIModel` for the documentation of parameters.
"""
def __init__(self, model_params):
model_params.setdefault('lattice', "Chain")
CouplingMPOModel.__init__(self, model_params)