"""This module contains some base classes for models.
A 'model' is supposed to represent a Hamiltonian in a generalized way.
The :class:`~tenpy.models.lattice.Lattice` specifies the geometry and
underlying Hilbert space, and is thus common to all models.
It is needed to intialize the common base class :class:`Model` of all models.
Different algorithms require different representations of the Hamiltonian.
For example for DMRG, the Hamiltonian needs to be given as an MPO,
while TEBD needs the Hamiltonian to be represented by 'nearest neighbor' bond terms.
This module contains the base classes defining these possible representations,
namley the :class:`MPOModel` and :class:`NearestNeighborModel`.
A particular model like the :class:`~tenpy.models.models.xxz_chain.XXZChain` should then
yet another class derived from these classes. In it's __init__, it needs to explicitly call
the ``MPOModel.__init__(self, lattice, H_MPO)``, providing an MPO representation of H,
and also the ``NearestNeighborModel.__init__(self, lattice, H_bond)``,
providing a representation of H by bond terms `H_bond`.
The :class:`CouplingModel` is the attempt to generalize the representation of `H`
by explicitly specifying the couplings in a general way, and providing functionality
for converting them into `H_MPO` and `H_bond`.
This allows to quickly generate new model classes for a very broad class of Hamiltonians.
For simplicity, the :class:`CouplingModel` is limited to interactions involving only two sites.
Yet, we also provide the :class:`MultiCouplingModel` to generate Models for Hamiltonians
involving couplings between multiple sites.
The :class:`CouplingMPOModel` aims at structuring the initialization for most models and is used
as base class in (most of) the predefined models in TeNPy.
See also the introduction in :doc:`/intro_model`.
"""
# Copyright 2018-2019 TeNPy Developers, GNU GPLv3
import numpy as np
import warnings
from .lattice import get_lattice, Lattice, TrivialLattice
from ..linalg import np_conserved as npc
from ..linalg.charges import QTYPE, LegCharge
from ..tools.misc import to_array, add_with_None_0
from ..tools.params import get_parameter, unused_parameters
from ..networks import mpo # used to construct the Hamiltonian as MPO
from ..networks.terms import OnsiteTerms, CouplingTerms, MultiCouplingTerms
from ..networks.terms import order_combine_term
from ..networks.site import group_sites
__all__ = [
'Model', 'NearestNeighborModel', 'MPOModel', 'CouplingModel', 'MultiCouplingModel',
'CouplingMPOModel'
]
[docs]class Model:
"""Base class for all models.
The common base to all models is the underlying Hilbert space and geometry, specified by a
:class:`~tenpy.model.lattice.Lattice`.
Parameters
----------
lattice : :class:`~tenpy.model.lattice.Lattice`
The lattice defining the geometry and the local Hilbert space(s).
Attributes
----------
lat : :class:`~tenpy.model.lattice.Lattice`
The lattice defining the geometry and the local Hilbert space(s).
"""
def __init__(self, lattice):
# NOTE: every subclass like CouplingModel, MPOModel, NearestNeighborModel calls this
# __init__, so it get's called multiple times when a user implements e.g. a
# class MyModel(CouplingModel, NearestNeighborModel, MPOModel).
if not hasattr(self, 'lat'):
# first call: initialize everything
self.lat = lattice
else:
# Model.__init__() got called before
if self.lat is not lattice: # expect the *same instance*!
raise ValueError("Model.__init__() called with different lattice instances.")
[docs] def group_sites(self, n=2, grouped_sites=None):
"""Modify `self` in place to group sites.
Group each `n` sites together using the :class:`~tenpy.networks.site.GroupedSite`.
This might allow to do TEBD with a Trotter decomposition,
or help the convergence of DMRG (in case of too long range interactions).
This has to be done after finishing initialization and can not be reverted.
Parameters
----------
n : int
Number of sites to be grouped together.
grouped_sites : None | list of :class:`~tenpy.networks.site.GroupedSite`
The sites grouped together.
Returns
-------
grouped_sites : list of :class:`~tenpy.networks.site.GroupedSite`
The sites grouped together.
"""
if grouped_sites is None:
grouped_sites = group_sites(self.lat.mps_sites(), n, charges='same')
else:
assert grouped_sites[0].n_sites == n
self.lat = TrivialLattice(grouped_sites, bc_MPS=self.lat.bc_MPS, bc='periodic')
return grouped_sites
[docs]class NearestNeighborModel(Model):
r"""Base class for a model of nearest neigbor interactions w.r.t. the MPS index.
In this class, the Hamiltonian :math:`H = \sum_{i} H_{i,i+1}` is represented by
"bond terms" :math:`H_{i,i+1}` acting only on two neighboring sites `i` and `i+1`,
where `i` is an integer.
Instances of this class are suitable for :mod:`~tenpy.algorithms.tebd`.
Note that the "nearest-neighbor" in the name referst to the MPS index, not the lattice.
In short, this works only for 1-dimensional (1D) nearest-neighbor models:
A 2D lattice is internally mapped to a 1D MPS "snake", and even a nearest-neighbor coupling
in 2D becomes long-range in the MPS chain.
Parameters
----------
lattice : :class:`tenpy.model.lattice.Lattice`
The lattice defining the geometry and the local Hilbert space(s).
H_bond : list of {:class:`~tenpy.linalg.np_conserved.Array` | None}
The Hamiltonian rewritten as ``sum_i H_bond[i]`` for MPS indices ``i``.
``H_bond[i]`` acts on sites ``(i-1, i)``; we require ``len(H_bond) == lat.N_sites``.
Legs of each ``H_bond[i]`` are ``['p0', 'p0*', 'p1', 'p1*']``.
Attributes
----------
H_bond : list of {:class:`~tenpy.linalg.np_conserved.Array` | None}
The Hamiltonian rewritten as ``sum_i H_bond[i]`` for MPS indices ``i``.
``H_bond[i]`` acts on sites ``(i-1, i)``, ``None`` represents 0.
Legs of each ``H_bond[i]`` are ``['p0', 'p0*', 'p1', 'p1*']``.
"""
def __init__(self, lattice, H_bond):
Model.__init__(self, lattice)
self.H_bond = list(H_bond)
if self.lat.bc_MPS != 'infinite':
assert self.H_bond[0] is None
NearestNeighborModel.test_sanity(self)
# like self.test_sanity(), but use the version defined below even for derived class
[docs] @classmethod
def from_MPOModel(cls, mpo_model):
"""Initialize a NearestNeighborModel from a model class defining an MPO.
This is especially usefull in combination with :meth:`MPOModel.group_sites`.
Parameters
----------
mpo_model : :class:`MPOModel`
A model instance implementing the MPO.
Does not need to be a :class:`NearestNeighborModel`, but should only have
nearest-neighbor couplings.
Examples
--------
The `SpinChainNNN2` has next-nearest-neighbor couplings and thus only implements an MPO:
>>> from tenpy.models.spins_nnn import SpinChainNNN2
>>> nnn_chain = SpinChainNNN2({'L': 20})
parameter 'L'=20 for SpinChainNNN2
>>> print(isinstance(nnn_chain, NearestNeighborModel))
False
>>> print("range before grouping:", nnn_chain.H_MPO.max_range)
range before grouping: 2
By grouping each two neighboring sites, we can bring it down to nearest neighbors.
>>> nnn_chain.group_sites(2)
>>> print("range after grouping:", nnn_chain.H_MPO.max_range)
range after grouping: 1
Yet, TEBD will not yet work, as the model doesn't define `H_bond`.
However, we can initialize a NearestNeighborModel from the MPO:
>>> nnn_chain_for_tebd = NearestNeighborModel.from_MPOModel(nnn_chain)
"""
return cls(mpo_model.lat, mpo_model.calc_H_bond_from_MPO())
def test_sanity(self):
if len(self.H_bond) != self.lat.N_sites:
raise ValueError("wrong len of H_bond")
[docs] def trivial_like_NNModel(self):
"""Return a NearestNeighborModel with same lattice, but trivial (H=0) bonds."""
triv_H = [H.zeros_like() if H is not None else None for H in self.H_bond]
return NearestNeighborModel(self.lat, triv_H)
[docs] def bond_energies(self, psi):
"""Calculate bond energies <psi|H_bond|psi>.
Parameters
----------
psi : :class:`~tenpy.networks.mps.MPS`
The MPS for which the bond energies should be calculated.
Returns
-------
E_bond : 1D ndarray
List of bond energies: for finite bc, ``E_Bond[i]`` is the energy of bond ``i, i+1``.
(i.e. we omit bond 0 between sites L-1 and 0);
for infinite bc ``E_bond[i]`` is the energy of bond ``i-1, i``.
"""
if self.lat.bc_MPS == 'infinite':
return psi.expectation_value(self.H_bond, axes=(['p0', 'p1'], ['p0*', 'p1*']))
# else
return psi.expectation_value(self.H_bond[1:], axes=(['p0', 'p1'], ['p0*', 'p1*']))
[docs] def group_sites(self, n=2, grouped_sites=None):
"""Modify `self` in place to group sites.
Group each `n` sites together using the :class:`~tenpy.networks.site.GroupedSite`.
This might allow to do TEBD with a Trotter decomposition,
or help the convergence of DMRG (in case of too long range interactions).
This has to be done after finishing initialization and can not be reverted.
Parameters
----------
n : int
Number of sites to be grouped together.
grouped_sites : None | list of :class:`~tenpy.networks.site.GroupedSite`
The sites grouped together.
Returns
-------
grouped_sites : list of :class:`~tenpy.networks.site.GroupedSite`
The sites grouped together.
"""
grouped_sites = super().group_sites(n, grouped_sites)
old_L = len(self.H_bond)
new_L = len(grouped_sites)
finite = self.H_bond[0] is None
H_bond = [None] * new_L
i = 0 # old index
for k, gs in enumerate(grouped_sites):
# calculate new_Hb on bond (k, k+1)
k2 = (k + 1) % new_L
next_gs = grouped_sites[k2]
new_H_onsite = None # collect old H_bond terms inside `gs`
for j in range(1, gs.n_sites):
old_Hb = self.H_bond[(i + j) % old_L]
add_H_onsite = self._group_sites_Hb_to_onsite(gs, j, old_Hb)
new_H_onsite = add_with_None_0(new_H_onsite, add_H_onsite)
old_Hb = self.H_bond[(i + gs.n_sites) % old_L]
new_Hb = self._group_sites_Hb_to_bond(gs, next_gs, old_Hb)
if new_H_onsite is not None:
if k + 1 != new_L or not finite:
# infinite or in the bulk: add new_H_onsite to new_Hb
add_Hb = npc.outer(new_H_onsite, next_gs.Id.transpose(['p', 'p*']))
new_Hb = add_with_None_0(new_Hb, add_Hb)
else: # finite and k = new_L - 1
# the new_H_onsite needs to be added to the right-most Hb
prev_gs = grouped_sites[k - 1]
add_Hb = npc.outer(prev_gs.Id.transpose(['p', 'p*']), new_H_onsite)
H_bond[-1] = add_with_None_0(H_bond[-1], add_Hb)
H_bond[k2] = add_with_None_0(H_bond[k2], new_Hb)
i += gs.n_sites
for Hb in H_bond:
if Hb is None:
continue
Hb.iset_leg_labels(['p0', 'p0*', 'p1', 'p1*']).itranspose(['p0', 'p1', 'p0*', 'p1*'])
self.H_bond = H_bond
return grouped_sites
def _group_sites_Hb_to_onsite(self, gr_site, j, old_Hb):
"""kroneckerproduct for H_bond term within a GroupedSite.
`old_Hb` acts on sites (j-1, j) of `gr_sites`.
"""
if old_Hb is None:
return None
old_Hb = old_Hb.transpose(['p0', 'p0*', 'p1', 'p1*'])
ops = [s.Id
for s in gr_site.sites[:j - 1]] + [old_Hb] + [s.Id for s in gr_site.sites[j + 1:]]
Hb = ops[0]
for op in ops[1:]:
Hb = npc.outer(Hb, op)
combine = [list(range(0, 2 * gr_site.n_sites, 2)), list(range(1, 2 * gr_site.n_sites, 2))]
pipe = gr_site.leg
Hb = Hb.combine_legs(combine, pipes=[pipe, pipe.conj()])
return Hb # labels would be 'p', 'p*' w.r.t. gr_site.
def _group_sites_Hb_to_bond(self, gr_site_L, gr_site_R, old_Hb):
"""Kroneckerproduct for H_bond term acting on two GroupedSites.
`old_Hb` acts on the right-most site of `gr_site_L` and left-most site of `gr_site_R`.
"""
if old_Hb is None:
return None
old_Hb = old_Hb.transpose(['p0', 'p0*', 'p1', 'p1*'])
ops = [s.Id for s in gr_site_L.sites[:-1]] + [old_Hb] + [s.Id for s in gr_site_R.sites[1:]]
Hb = ops[0]
for op in ops[1:]:
Hb = npc.outer(Hb, op)
NL, NR = gr_site_L.n_sites, gr_site_R.n_sites
pipeL, pipeR = gr_site_L.leg, gr_site_R.leg
combine = [
list(range(0, 2 * NL, 2)),
list(range(1, 2 * NL, 2)),
list(range(2 * NL, 2 * (NL + NR), 2)),
list(range(2 * NL + 1, 2 * (NL + NR), 2))
]
Hb = Hb.combine_legs(combine, pipes=[pipeL, pipeL.conj(), pipeR, pipeR.conj()])
return Hb # labels would be 'p0', 'p0*', 'p1', 'p1*' w.r.t. gr_site_{L,R}
[docs] def calc_H_MPO_from_bond(self, tol_zero=1.e-15):
"""Calculate the MPO Hamiltonian from the bond Hamiltonian.
Parameters
----------
tol_zero : float
Arrays with norm < `tol_zero` are considered to be zero.
Returns
-------
H_MPO : :class:`~tenpy.networks.mpo.MPO`
MPO representation of the Hamiltonian.
"""
H_bond = self.H_bond # entry i acts on sites (i-1,i)
dtype = np.find_common_type([Hb.dtype for Hb in H_bond if Hb is not None], [])
bc = self.lat.bc_MPS
sites = self.lat.mps_sites()
L = len(sites)
onsite_terms = [None] * L # onsite terms on each site `i`
bond_XYZ = [None] * L # svd of couplings on each bond (i-1, i)
chis = [2] * (L + 1)
assert len(self.H_bond) == L
for i, Hb in enumerate(H_bond):
if Hb is None:
continue
j = (i - 1) % L
Hb = Hb.transpose(['p0', 'p0*', 'p1', 'p1*'])
d_L, d_R = sites[j].dim, sites[i].dim # dimension of local hilbert space:
Id_L, Id_R = sites[i].Id, sites[j].Id
# project on onsite-terms by contracting with identities; Tr(Id_{L/R}) = d_{L/R}
onsite_L = npc.tensordot(Hb, Id_R, axes=(['p1', 'p1*'], ['p*', 'p'])) / d_R
if npc.norm(onsite_L) > tol_zero:
Hb -= npc.outer(onsite_L, Id_R)
onsite_terms[j] = add_with_None_0(onsite_terms[j], onsite_L)
onsite_R = npc.tensordot(Id_L, Hb, axes=(['p*', 'p'], ['p0', 'p0*'])) / d_L
if npc.norm(onsite_R) > tol_zero:
Hb -= npc.outer(Id_L, onsite_R)
onsite_terms[i] = add_with_None_0(onsite_terms[i], onsite_R)
if npc.norm(Hb) < tol_zero:
continue
Hb = Hb.combine_legs([['p0', 'p0*'], ['p1', 'p1*']])
chinfo = Hb.chinfo
qtotal = [chinfo.make_valid(), chinfo.make_valid()] # zero charge
X, Y, Z = npc.svd(Hb, cutoff=tol_zero, inner_labels=['wR', 'wL'], qtotal_LR=qtotal)
assert len(Y) > 0
chis[i] = len(Y) + 2
X = X.split_legs([0])
YZ = Z.iscale_axis(Y, axis=0).split_legs([1])
bond_XYZ[i] = (X, YZ)
chinfo = Hb.chinfo
# construct the legs
legs = [None] * (L + 1) # legs[i] is leg 'wL' left of site i with qconj=+1
for i in range(L + 1):
if i == L and bc == 'infinite':
legs[i] = legs[0]
break
chi = chis[i]
qflat = np.zeros((chi, chinfo.qnumber), dtype=QTYPE)
if chi > 2:
YZ = bond_XYZ[i][1]
qflat[1:-1, :] = Z.legs[0].to_qflat()
leg = LegCharge.from_qflat(chinfo, qflat, qconj=+1)
legs[i] = leg
# now construct the W tensors
Ws = [None] * L
for i in range(L):
wL, wR = legs[i], legs[i + 1].conj()
p = sites[i].leg
W = npc.zeros([wL, wR, p, p.conj()], dtype)
W[0, 0, :, :] = sites[i].Id
W[-1, -1, :, :] = sites[i].Id
onsite = onsite_terms[i]
if onsite is not None:
W[0, -1, :, :] = onsite
if bond_XYZ[i] is not None:
_, YZ = bond_XYZ[i]
W[1:-1, -1, :, :] = YZ.itranspose(['wL', 'p1', 'p1*'])
j = (i + 1) % L
if bond_XYZ[j] is not None:
X, _ = bond_XYZ[j]
W[0, 1:-1, :, :] = X.itranspose(['wR', 'p0', 'p0*'])
W.iset_leg_labels(['wL', 'wR', 'p', 'p*'])
Ws[i] = W
H_MPO = mpo.MPO(sites, Ws, bc, 0, -1, max_range=2)
return H_MPO
[docs]class MPOModel(Model):
"""Base class for a model with an MPO representation of the Hamiltonian.
In this class, the Hamiltonian gets represented by an :class:`~tenpy.networks.mpo.MPO`.
Thus, instances of this class are suitable for MPO-based algorithms like DMRG
:mod:`~tenpy.algorithms.dmrg` and MPO time evolution.
.. todo ::
implement MPO for time evolution...
Parameters
----------
H_MPO : :class:`~tenpy.networks.mpo.MPO`
The Hamiltonian rewritten as an MPO.
Attributes
----------
H_MPO : :class:`tenpy.networks.mpo.MPO`
MPO representation of the Hamiltonian.
"""
def __init__(self, lattice, H_MPO):
Model.__init__(self, lattice)
self.H_MPO = H_MPO
MPOModel.test_sanity(self)
# like self.test_sanity(), but use the version defined below even for derived class
def test_sanity(self):
if self.H_MPO.sites != self.lat.mps_sites():
raise ValueError("lattice incompatible with H_MPO.sites")
[docs] def group_sites(self, n=2, grouped_sites=None):
"""Modify `self` in place to group sites.
Group each `n` sites together using the :class:`~tenpy.networks.site.GroupedSite`.
This might allow to do TEBD with a Trotter decomposition,
or help the convergence of DMRG (in case of too long range interactions).
This has to be done after finishing initialization and can not be reverted.
Parameters
----------
n : int
Number of sites to be grouped together.
grouped_sites : None | list of :class:`~tenpy.networks.site.GroupedSite`
The sites grouped together.
Returns
-------
grouped_sites : list of :class:`~tenpy.networks.site.GroupedSite`
The sites grouped together.
"""
grouped_sites = super().group_sites(n, grouped_sites)
self.H_MPO.group_sites(n, grouped_sites)
return grouped_sites
[docs] def calc_H_bond_from_MPO(self, tol_zero=1.e-15):
"""Calculate the bond Hamiltonian from the MPO Hamiltonian.
Parameters
----------
tol_zero : float
Arrays with norm < `tol_zero` are considered to be zero.
Returns
-------
H_bond : list of :class:`~tenpy.linalg.np_conserved.Array`
Bond terms as required by the constructor of :class:`NearestNeighborModel`.
Legs are ``['p0', 'p0*', 'p1', 'p1*']``
Raises
------
ValueError : if the Hamiltonian contains longer-range terms.
"""
H_MPO = self.H_MPO
sites = H_MPO.sites
finite = H_MPO.finite
L = H_MPO.L
Ws = [H_MPO.get_W(i, copy=True) for i in range(L)]
# Copy of Ws: we set everything to zero, which we take out and add to H_bond, such that
# we can check that Ws is zero in the end to ensure that H didn't have long range couplings
H_onsite = [None] * L
H_bond = [None] * L
# first take out onsite terms and identities
for i, W in enumerate(Ws):
# bond `a` is left of site i, bond `b` is right
IdL_a = H_MPO.IdL[i]
IdR_a = H_MPO.IdR[i]
IdL_b = H_MPO.IdL[i + 1]
IdR_b = H_MPO.IdR[i + 1]
W.itranspose(['wL', 'wR', 'p', 'p*'])
H_onsite[i] = W[IdL_a, IdR_b, :, :]
W[IdL_a, IdR_b, :, :] *= 0
# remove Identities
if IdR_a is not None:
W[IdR_a, IdR_b, :, :] *= 0.
if IdL_b is not None:
W[IdL_a, IdL_b, :, :] *= 0.
# now multiply together the bonds
for j, Wj in enumerate(Ws):
# for bond (i, j) == (j-1, j) == (i, i+1)
if finite and j == 0:
continue
i = (j - 1) % L
Wi = Ws[i]
IdL_a = H_MPO.IdL[i]
IdR_c = H_MPO.IdR[j + 1]
Hb = npc.tensordot(Wi[IdL_a, :, :, :], Wj[:, IdR_c, :, :], axes=('wR', 'wL'))
Wi[IdL_a, :, :, :] *= 0.
Wj[:, IdR_c, :, :] *= 0.
# Hb has legs p0, p0*, p1, p1*
H_bond[j] = Hb
# check that nothing is left
for W in Ws:
if npc.norm(W) > tol_zero:
raise ValueError("Bond couplings didn't capture everything. "
"Either H is long range or IdL/IdR is wrong!")
# now merge the onsite terms to H_bond
for j in range(L):
if finite and j == 0:
continue
i = (j - 1) % L
strength_i = 1. if finite and i == 0 else 0.5
strength_j = 1. if finite and j == L - 1 else 0.5
Hb = (npc.outer(sites[i].Id, strength_j * H_onsite[j]) +
npc.outer(strength_i * H_onsite[i], sites[j].Id))
Hb = add_with_None_0(H_bond[j], Hb)
Hb.iset_leg_labels(['p0', 'p0*', 'p1', 'p1*'])
H_bond[j] = Hb
if finite:
assert H_bond[0] is None
return H_bond
[docs]class CouplingModel(Model):
"""Base class for a general model of a Hamiltonian consisting of two-site couplings.
In this class, the terms of the Hamiltonian are specified explicitly as
:class:`~tenpy.networks.terms.OnsiteTerms` or :class:`~tenpy.networks.terms.CouplingTerms`.
.. deprecated:: 0.4.0
`bc_coupling` will be removed in 1.0.0. To specify the full geometry in the lattice,
use the `bc` parameter of the :class:`~tenpy.model.latttice.Lattice`.
Parameters
----------
lattice : :class:`~tenpy.model.lattice.Lattice`
The lattice defining the geometry and the local Hilbert space(s).
bc_coupling : (iterable of) {``'open'`` | ``'periodic'`` | ``int``}
Boundary conditions of the couplings in each direction of the lattice. Defines how the
couplings are added in :meth:`add_coupling`. A single string holds for all directions.
An integer `shift` means that we have periodic boundary conditions along this direction,
but shift/tilt by ``-shift*lattice.basis[0]`` (~cylinder axis for ``bc_MPS='infinite'``)
when going around the boundary along this direction.
Attributes
----------
onsite_terms : {'category': :class:`~tenpy.networks.terms.OnsiteTerms`}
The :class:`~tenpy.networks.terms.OnsiteTerms` ordered by category.
coupling_terms : {'category': :class:`~tenpy.networks.terms.CouplingTerms`}
The :class:`~tenpy.networks.terms.CouplingTerms` ordered by category.
In a :class:`MultiCouplingModel`, values may also be
:class:`~tenpy.networks.terms.MultiCouplingTerms`.
"""
def __init__(self, lattice, bc_coupling=None):
Model.__init__(self, lattice)
if bc_coupling is not None:
warnings.warn("`bc_coupling` in CouplingModel: use `bc` in Lattice instead",
FutureWarning,
stacklevel=2)
lattice._set_bc(bc_coupling)
L = self.lat.N_sites
self.onsite_terms = {}
self.coupling_terms = {}
CouplingModel.test_sanity(self)
# like self.test_sanity(), but use the version defined below even for derived class
[docs] def test_sanity(self):
"""Sanity check, raises ValueErrors, if something is wrong."""
sites = self.lat.mps_sites()
for ot in self.onsite_terms.values():
ot._test_terms(sites)
for ct in self.coupling_terms.values():
ct._test_terms(sites)
[docs] def add_onsite(self, strength, u, opname, category=None):
r"""Add onsite terms to :attr:`onsite_terms`.
Adds a term :math:`\sum_{x_0, ..., x_{dim-1}} strength[x_0, ..., x_{dim-1}] * OP``,
where the operator ``OP=lat.unit_cell[u].get_op(opname)``
acts on the site given by a lattice index ``(x_0, ..., x_{dim-1}, u)``,
to the represented Hamiltonian.
The necessary terms are just added to :attr:`onsite_terms`; doesn't rebuild the MPO.
Parameters
----------
strength : scalar | array
Prefactor of the onsite term. May vary spatially. If an array of smaller size
is provided, it gets tiled to the required shape.
u : int
Picks a :class:`~tenpy.model.lattice.Site` ``lat.unit_cell[u]`` out of the unit cell.
opname : str
valid operator name of an onsite operator in ``lat.unit_cell[u]``.
category : str
Descriptive name used as key for :attr:`onsite_terms`. Defaults to `opname`.
"""
strength = to_array(strength, self.lat.Ls) # tile to lattice shape
if not np.any(strength != 0.):
return # nothing to do: can even accept non-defined `opname`.
if not self.lat.unit_cell[u].valid_opname(opname):
raise ValueError("unknown onsite operator {0!r} for u={1:d}\n"
"{2!r}".format(opname, u, self.lat.unit_cell[u]))
if category is None:
category = opname
ot = self.onsite_terms.get(category, None)
if ot is None:
self.onsite_terms[category] = ot = OnsiteTerms(self.lat.N_sites)
for i, i_lat in zip(*self.lat.mps_lat_idx_fix_u(u)):
ot.add_onsite_term(strength[tuple(i_lat)], i, opname)
[docs] def add_onsite_term(self, strength, i, op, category=None):
"""Add an onsite term on a given MPS site.
Wrapper for ``self.onsite_terms[category].add_onsite_term(...)``.
Parameters
----------
strength : float
The strength of the term.
i : int
The MPS index of the site on which the operator acts.
We require ``0 <= i < L``.
op : str
Name of the involved operator.
category : str
Descriptive name used as key for :attr:`onsite_terms`. Defaults to `op`.
"""
if category is None:
category = op
ot = self.onsite_terms.get(category, None)
if ot is None:
self.onsite_terms[category] = ot = OnsiteTerms(self.lat.N_sites)
ot.add_onsite_term(strength, i, op)
[docs] def all_onsite_terms(self):
"""Sum of all :attr:`onsite_terms`."""
sites = self.lat.mps_sites()
ot = OnsiteTerms(len(sites))
for t in self.onsite_terms.values():
ot += t
return ot
[docs] def add_coupling(self,
strength,
u1,
op1,
u2,
op2,
dx,
op_string=None,
str_on_first=True,
raise_op2_left=False,
category=None):
r"""Add twosite coupling terms to the Hamiltonian, summing over lattice sites.
Represents couplings of the form
:math:`\sum_{x_0, ..., x_{dim-1}} strength[loc(\vec{x})] * OP1 * OP2`, where
``OP1 := lat.unit_cell[u1].get_op(op1)`` acts on the site ``(x_0, ..., x_{dim-1}, u1)``,
and ``OP2 := lat.unit_cell[u2].get_op(op2)`` acts on the site
``(x_0+dx[0], ..., x_{dim-1}+dx[dim-1], u2)``.
Possible combinations ``x_0, ..., x_{dim-1}`` are determined from the boundary conditions
in :meth:`~tenpy.models.lattice.Lattice.possible_couplings`.
The coupling `strength` may vary spatially, :math:`loc(\vec{x})` indicates the lower
left corner of the hypercube containing the involved sites :math:`\vec{x}` and
:math:`\vec{x}+\vec{dx}`.
The necessary terms are just added to :attr:`coupling_terms`; doesn't (re)build the MPO.
.. deprecated:: 0.4.0
The arguments `str_on_first` and `raise_op2_left` will be removed in version 1.0.0.
Parameters
----------
strength : scalar | array
Prefactor of the coupling. May vary spatially (see above). If an array of smaller size
is provided, it gets tiled to the required shape.
u1 : int
Picks the site ``lat.unit_cell[u1]`` for OP1.
op1 : str
Valid operator name of an onsite operator in ``lat.unit_cell[u1]`` for OP1.
u2 : int
Picks the site ``lat.unit_cell[u2]`` for OP2.
op2 : str
Valid operator name of an onsite operator in ``lat.unit_cell[u2]`` for OP2.
dx : iterable of int
Translation vector (of the unit cell) between OP1 and OP2.
For a 1D lattice, a single int is also fine.
op_string : str | None
Name of an operator to be used between the OP1 and OP2 sites.
Typical use case is the phase for a Jordan-Wigner transformation.
The operator should be defined on all sites in the unit cell.
If ``None``, auto-determine whether a Jordan-Wigner string is needed, using
:meth:`~tenpy.networks.site.Site.op_needs_JW`.
str_on_first : bool
Whether the provided `op_string` should also act on the first site.
This option should be chosen as ``True`` for Jordan-Wigner strings.
When handling Jordan-Wigner strings we need to extend the `op_string` to also act on
the 'left', first site (in the sense of the MPS ordering of the sites given by the
lattice). In this case, there is a well-defined ordering of the operators in the
physical sense (i.e. which of `op1` or `op2` acts first on a given state).
We follow the convention that `op2` acts first (in the physical sense),
independent of the MPS ordering.
Deprecated.
raise_op2_left : bool
Raise an error when `op2` appears left of `op1`
(in the sense of the MPS ordering given by the lattice). Deprecated.
category : str
Descriptive name used as key for :attr:`coupling_terms`.
Defaults to a string of the form ``"{op1}_i {op2}_j"``.
Examples
--------
When initializing a model, you can add a term :math:`J \sum_{<i,j>} S^z_i S^z_j`
on all nearest-neighbor bonds of the lattice like this:
>>> J = 1. # the strength
>>> for u1, u2, dx in self.lat.pairs['nearest_neighbors']:
... self.add_coupling(J, u1, 'Sz', u2, 'Sz', dx)
The strength can be an array, which get's tiled to the correct shape.
For example, in a 1D :class:`~tenpy.models.lattice.Chain` with an even number of sites and
periodic (or infinite) boundary conditions, you can add alternating strong and weak
couplings with a line like::
>>> self.add_coupling([1.5, 1.], 0, 'Sz', 0, 'Sz', dx)
To add the hermitian conjugate, e.g. for a hopping term, you should add it in the opposite
direction ``-dx``, complex conjugate the strength, and take the hermitian conjugate
of the operators in swapped order (including a swap of `u1` <-> `u2`).
For spin-less fermions (:class:`~tenpy.networks.site.FermionSite`), this would be
>>> t = 1. # hopping strength
>>> for u1, u2, dx in self.lat.pairs['nearest_neighbors']:
... self.add_coupling(t, u1, 'Cd', u2, 'C', dx)
... self.add_coupling(np.conj(t), u2, 'Cd', u1, 'C', -dx) # h.c.
With spin-full fermions (:class:`~tenpy.networks.site.SpinHalfFermions`), it could be:
>>> for u1, u2, dx in self.lat.pairs['nearest_neighbors']:
... self.add_coupling(t, u1, 'Cdu', u2, 'Cd', dx) # Cdagger_up C_down
... self.add_coupling(np.conj(t), u2, 'Cdd', u1, 'Cu', -dx) # h.c. Cdagger_down C_up
Note that the Jordan-Wigner strings are figured out automatically!
"""
dx = np.array(dx, np.intp).reshape([self.lat.dim])
if not np.any(np.asarray(strength) != 0.):
return # nothing to do: can even accept non-defined onsite operators
for op, u in [(op1, u1), (op2, u2)]:
if not self.lat.unit_cell[u].valid_opname(op):
raise ValueError(("unknown onsite operator {0!r} for u={1:d}\n"
"{2!r}").format(op, u, self.lat.unit_cell[u]))
site1 = self.lat.unit_cell[u1]
site2 = self.lat.unit_cell[u2]
if op_string is None:
need_JW1 = site1.op_needs_JW(op1)
need_JW2 = site2.op_needs_JW(op2)
if need_JW1 and need_JW2:
op_string = 'JW'
str_on_first = True
elif need_JW1 or need_JW2:
raise ValueError("Only one of the operators needs a Jordan-Wigner string?!")
else:
op_string = 'Id'
for u in range(len(self.lat.unit_cell)):
if not self.lat.unit_cell[u].valid_opname(op_string):
raise ValueError("unknown onsite operator {0!r} for u={1:d}\n"
"{2!r}".format(op_string, u, self.lat.unit_cell[u]))
if op_string == "JW" and not str_on_first:
raise ValueError("Jordan Wigner string without `str_on_first`")
if np.all(dx == 0) and u1 == u2:
raise ValueError("Coupling shouldn't be onsite!")
mps_i, mps_j, lat_indices, strength_shape = self.lat.possible_couplings(u1, u2, dx)
strength = to_array(strength, strength_shape) # tile to correct shape
if category is None:
category = "{op1}_i {op2}_j".format(op1=op1, op2=op2)
ct = self.coupling_terms.get(category, None)
if ct is None:
self.coupling_terms[category] = ct = CouplingTerms(self.lat.N_sites)
# loop to perform the sum over {x_0, x_1, ...}
for i, j, lat_idx in zip(mps_i, mps_j, lat_indices):
current_strength = strength[tuple(lat_idx)]
if current_strength == 0.:
continue
# the following is roughly equivalent to
# CouplingTerms.coupling_term_handle_JW, but also swaps i <-> j if necessary
# and allows `str_on_first` being set explicitly
o1, o2 = op1, op2
site_i = site1
if j < i: # ensure i <= j
# swap operators
i, j = j, i
if op_string == 'JW':
current_strength = -current_strength # swap sign
if raise_op2_left:
raise ValueError("Op2 is left")
o1, o2 = op2, op1
site_i = site2
# now we have always i < j and 0 <= i < N_sites
# j >= N_sites indicates couplings between unit_cells of the infinite MPS.
# o1 is the "left" operator; o2 is the "right" operator
if str_on_first and op_string != 'Id':
o1 = site_i.multiply_op_names([o1, op_string])
ct.add_coupling_term(current_strength, i, j, o1, o2, op_string)
# done
[docs] def add_coupling_term(self, strength, i, j, op_i, op_j, op_string='Id', category=None):
"""Add a two-site coupling term on given MPS sites.
Wrapper for ``self.coupling_terms[category].add_coupling_term(...)``.
Parameters
----------
strength : float
The strength of the coupling term.
i, j : int
The MPS indices of the two sites on which the operator acts.
We require ``0 <= i < N_sites`` and ``i < j``, i.e., `op_i` acts "left" of `op_j`.
If j >= N_sites, it indicates couplings between unit cells of an infinite MPS.
op1, op2 : str
Names of the involved operators.
op_string : str
The operator to be inserted between `i` and `j`.
category : str
Descriptive name used as key for :attr:`coupling_terms`.
Defaults to a string of the form ``"{op1}_i {op2}_j"``.
"""
if category is None:
category = "{op_i}_i {op_j}_j".format(op_i=op_i, op_j=op_j)
ct = self.coupling_terms.get(category, None)
if ct is None:
self.coupling_terms[category] = ct = CouplingTerms(self.lat.N_sites)
ct.add_coupling_term(strength, i, j, op_i, op_j, op_string)
[docs] def all_coupling_terms(self):
"""Sum of all :attr:`coupling_terms`."""
sites = self.lat.mps_sites()
if any([isinstance(ct, MultiCouplingTerms) for ct in self.coupling_terms.values()]):
ct = MultiCouplingTerms(len(sites))
else:
ct = CouplingTerms(len(sites))
for t in self.coupling_terms.values():
ct += t
return ct
[docs] def calc_H_onsite(self, tol_zero=1.e-15):
"""Calculate `H_onsite` from `self.onsite_terms`.
.. deprecated:: 0.4.0
This function will be removed in 1.0.0.
Replace calls to this function by
``self.all_onsite_terms().remove_zeros(tol_zero).to_Arrays(self.lat.mps_sites())``.
Parameters
----------
tol_zero : float
prefactors with ``abs(strength) < tol_zero`` are considered to be zero.
Returns
-------
H_onsite : list of npc.Array
onsite terms of the Hamiltonian.
"""
warnings.warn("Deprecated `calc_H_onsite` in CouplingModel", FutureWarning, stacklevel=2)
ot = self.all_onsite_terms()
ot.remove_zeros(tol_zero)
return ot.to_Arrays(self.lat.mps_sites())
[docs] def calc_H_bond(self, tol_zero=1.e-15):
"""calculate `H_bond` from :attr:`coupling_terms` and :attr:`onsite_terms`.
Parameters
----------
tol_zero : float
prefactors with ``abs(strength) < tol_zero`` are considered to be zero.
Returns
-------
H_bond : list of :class:`~tenpy.linalg.np_conserved.Array`
Bond terms as required by the constructor of :class:`NearestNeighborModel`.
Legs are ``['p0', 'p0*', 'p1', 'p1*']``
Raises
------
ValueError : if the Hamiltonian contains longer-range terms.
"""
sites = self.lat.mps_sites()
finite = (self.lat.bc_MPS != 'infinite')
ct = self.all_coupling_terms()
ct.remove_zeros(tol_zero)
H_bond = ct.to_nn_bond_Arrays(sites)
ot = self.all_onsite_terms()
ot.remove_zeros(tol_zero)
ot.add_to_nn_bond_Arrays(H_bond, sites, finite, distribute=(0.5, 0.5))
if finite:
assert H_bond[0] is None
return H_bond
[docs] def calc_H_MPO(self, tol_zero=1.e-15):
"""Calculate MPO representation of the Hamiltonian.
Uses :attr:`onsite_terms` and :attr:`coupling_terms` to build an MPO graph
(and then an MPO).
Parameters
----------
tol_zero : float
Prefactors with ``abs(strength) < tol_zero`` are considered to be zero.
Returns
-------
H_MPO : :class:`~tenpy.networks.mpo.MPO`
MPO representation of the Hamiltonian.
"""
ot = self.all_onsite_terms()
ot.remove_zeros(tol_zero)
ct = self.all_coupling_terms()
ct.remove_zeros(tol_zero)
self.H_MPO_graph = mpo.MPOGraph.from_terms(ot, ct, self.lat.mps_sites(), self.lat.bc_MPS)
H_MPO = self.H_MPO_graph.build_MPO()
H_MPO.max_range = ct.max_range()
return H_MPO
[docs] def coupling_strength_add_ext_flux(self, strength, dx, phase):
"""Add an external flux to the coupling strength.
When performing DMRG on a "cylinder" geometry, it might be useful to put an "external flux"
through the cylinder. This means that a particle hopping around the cylinder should
pick up a phase given by the external flux [Resta1997]_.
This is also called "twisted boundary conditions" in literature.
This function adds a complex phase to the `strength` array on some bonds, such that
particles hopping in positive direction around the cylinder pick up `exp(+i phase)`.
.. warning ::
For the sign of `phase` it is important that you consistently use the creation
operator as `op1` and the annihilation operator as `op2` in :meth:`add_coupling`.
Parameters
----------
strength : scalar | array
The strength to be used in :meth:`add_coupling`, when no external flux would be
present.
dx : iterable of int
Translation vector (of the unit cell) between `op1` and `op2` in :meth:`add_coupling`.
phase : iterable of float
The phase of the external flux for hopping in each direction of the lattice.
E.g., if you want flux through the cylinder on which you have an infinite MPS,
you should give ``phase=[0, phi]`` souch that particles pick up a phase `phi` when
hopping around the cylinder.
Returns
-------
strength : complex array
The strength array to be used as `strength` in :meth:`add_coupling`
with the given `dx`.
Examples
--------
Let's say you have an infinite MPS on a cylinder, and want to add nearest-neighbor
hopping of fermions with the :class:`~tenpy.networks.site.FermionSite`.
The cylinder axis is the `x`-direction of the lattice, so to put a flux through the
cylinder, you want particles hopping *around* the cylinder to pick up a phase `phi`
given by the external flux.
>>> strength = 1. # hopping strength without external flux
>>> phi = np.pi/4 # determines the external flux strength
>>> strength_with_flux = self.coupling_strength_add_ext_flux(strength, dx, [0, phi])
>>> for u1, u2, dx in self.lat.pairs['nearest_neighbors']:
... self.add_coupling(strength_with_flux, u1, 'Cd', u2, 'C', dx)
... self.add_coupling(np.conj(strength_with_flux), u2, 'Cd', u1, 'C', -dx)
"""
c_shape = self.lat.coupling_shape(dx)[0]
strength = to_array(strength, c_shape)
# make strenght complex
complex_dtype = np.find_common_type([strength.dtype], [np.dtype(np.complex)])
strength = np.asarray(strength, complex_dtype)
for ax in range(self.lat.dim):
if self.lat.bc[ax]: # open boundary conditions
if phase[ax]:
raise ValueError("Nonzero phase for external flux along non-periodic b.c.")
continue
if abs(dx[ax]) == 0:
continue # nothing to do
slices = [slice(None) for _ in range(self.lat.dim)]
slices[ax] = slice(-abs(dx[ax]), None)
# the last ``abs(dx[ax])`` entries in the axis `ax` correspond to hopping
# accross the periodic b.c.
slices = tuple(slices)
if dx[ax] > 0:
strength[slices] *= np.exp(-1.j * phase[ax]) # hopping in *negative* y-direction
else:
strength[slices] *= np.exp(1.j * phase[ax]) # hopping in *positive* y-direction
return strength
[docs]class MultiCouplingModel(CouplingModel):
"""Generalizes :class:`CouplingModel` to allow couplings involving more than two sites.
The corresponding couplings can be added with :meth:`add_multi_coupling` and
:meth:`add_multi_coupling_term` and are saved in :attr:`coupling_terms`, which can now contain
instances of :class:`~tenpy.networks.terms.MultiCouplingTerms`.
"""
[docs] def add_multi_coupling(self, strength, u0, op0, other_ops, op_string=None, category=None):
r"""Add multi-site coupling terms to the Hamiltonian, summing over lattice sites.
Represents couplings of the form
:math:`sum_{x_0, ..., x_{dim-1}} strength[loc(\vec{x})] * OP0 * OP1 * ... * OPM`,
where ``OP_0 := lat.unit_cell[u0].get_op(op0)`` acts on the site
``(x_0, ..., x_{dim-1}, u0)``,
and ``OP_m := lat.unit_cell[other_u[m]].get_op(other_op[m])``, m=1...M, acts on the site
``(x_0+other_dx[m][0], ..., x_{dim-1}+other_dx[m][dim-1], other_u[m])``.
For periodic boundary conditions along direction `a` (``lat.bc[a] == False``)
the index ``x_a`` is taken modulo ``lat.Ls[a]`` and runs through ``range(lat.Ls[a])``.
For open boundary conditions, ``x_a`` is limited to ``0 <= x_a < Ls[a]`` and
``0 <= x_a+other_dx[m,a] < lat.Ls[a]``.
The coupling `strength` may vary spatially, :math:`loc(\vec{x})` indicates the lower left
corner of the hypercube containing all the involved sites
:math:`\vec{x}, \vec{x}+\vec{other_dx[m, :]}`.
The necessary terms are just added to :attr:`coupling_terms`; doesn't rebuild the MPO.
Parameters
----------
strength : scalar | array
Prefactor of the coupling. May vary spatially and is tiled to the required shape.
u0 : int
Picks the site ``lat.unit_cell[u0]`` for OP0.
op0 : str
Valid operator name of an onsite operator in ``lat.unit_cell[u0]`` for OP0.
other_ops : list of ``(u, op_m, dx)``
One tuple for each of the other operators ``OP1, OP2, ... OPM`` involved.
`u` picks the site ``lat.unit_cell[u]``, `op_name` is a valid operator acting on that
site, and `dx` gives the translation vector between ``OP0`` and the specified operator.
op_string : str | None
Name of an operator to be used inbetween the operators, excluding the sites on which
the operators act. This operator should be defined on all sites in the unit cell.
Special case: If ``None``, auto-determine whether a Jordan-Wigner string is needed
(using :meth:`~tenpy.networks.site.Site.op_needs_JW`), for each of the segments
inbetween the operators and also on the sites of the left operators.
Note that in this case the ordering of the operators *is* important and handled in the
usual convention that ``OPM`` acts first and ``OP0`` last on a physical state.
.. warning :
``None`` figures out for each segment between the operators, whether a
Jordan-Wigner string is needed.
This is different from a plain ``'JW'``, which just applies a string on
each segment!
category : str
Descriptive name used as key for :attr:`coupling_terms`.
Defaults to a string of the form ``"{op0}_i {other_ops[0]}_j {other_ops[1]}_k ..."``.
"""
other_ops = list(other_ops)
M = len(other_ops)
all_us = np.array([u0] + [oop[0] for oop in other_ops], np.intp)
all_ops = [op0] + [oop[1] for oop in other_ops]
dx = np.array([oop[2] for oop in other_ops], np.intp).reshape([M, self.lat.dim])
if not np.any(strength != 0.):
return # nothing to do: can even accept non-defined onsite operators
need_JW = np.array(
[self.lat.unit_cell[u].op_needs_JW(op) for u, op in zip(all_us, all_ops)],
dtype=np.bool_)
if not np.sum(need_JW) % 2 == 0:
raise ValueError("Invalid coupling: would need 'JW' string on the very left")
if op_string is None and not any(need_JW):
op_string = 'Id'
for u, op, _ in [(u0, op0, None)] + other_ops:
if not self.lat.unit_cell[u].valid_opname(op):
raise ValueError("unknown onsite operator {0!r} for u={1:d}\n"
"{2!r}".format(op, u, self.lat.unit_cell[u]))
if op_string is not None:
for u in range(len(self.lat.unit_cell)):
if not self.lat.unit_cell[u].valid_opname(op_string):
raise ValueError("unknown onsite operator {0!r} for u={1:d}\n"
"{2!r}".format(op_string, u, self.lat.unit_cell[u]))
if np.all(dx == 0) and np.all(u0 == all_us):
# note: we DO allow couplings with some onsite terms, but not all of them
raise ValueError("Coupling shouldn't be purely onsite!")
# prepare: figure out the necessary mps indices
mps_ijkl, lat_indices, strength_shape = self.lat.possible_multi_couplings(
u0, all_us[1:], dx)
strength = to_array(strength, strength_shape) # tile to correct shape
if category is None:
category = " ".join(
["{op}_{i}".format(op=op, i=chr(ord('i') + m)) for m, op in enumerate(all_ops)])
ct = self.coupling_terms.get(category, None)
if ct is None:
self.coupling_terms[category] = ct = MultiCouplingTerms(self.lat.N_sites)
elif not isinstance(ct, MultiCouplingTerms):
self.coupling_terms[category] = new_ct = MultiCouplingTerms(self.lat.N_sites)
new_ct += ct
ct = new_ct
N_sites = self.lat.N_sites
sites = self.lat.mps_sites()
# loop to perform the sum over {x_0, x_1, ...}
for ijkl, i_lat in zip(mps_ijkl, lat_indices):
current_strength = strength[tuple(i_lat)]
if current_strength == 0.:
continue
term = list(zip(all_ops, ijkl))
term, sign = order_combine_term(term, sites)
args = ct.multi_coupling_term_handle_JW(current_strength * sign, term, sites,
op_string)
ct.add_multi_coupling_term(*args)
# done
[docs] def add_multi_coupling_term(self, strength, ijkl, ops_ijkl, op_string, category=None):
"""Add a general M-site coupling term on given MPS sites.
Wrapper for ``self.coupling_terms[category].add_multi_coupling_term(...)``.
Parameters
----------
strength : float
The strength of the coupling term.
ijkl : list of int
The MPS indices of the sites on which the operators acts. With `i, j, k, ... = ijkl`,
we require that they are ordered ascending, ``i < j < k < ...`` and
that ``0 <= i < N_sites``.
Inidces >= N_sites indicate couplings between different unit cells of an infinite MPS.
ops_ijkl : list of str
Names of the involved operators on sites `i, j, k, ...`.
op_string : list of str
Names of the operator to be inserted between the operators,
e.g., op_string[0] is inserted between `i` and `j`.
category : str
Descriptive name used as key for :attr:`coupling_terms`.
Defaults to a string of the form ``"{op0}_i {other_ops[0]}_j {other_ops[1]}_k ..."``.
"""
if category is None:
category = " ".join(
["{op}_{i}".format(op=op, i=chr(ord('i') + m)) for m, op in enumerate(ops_ijkl)])
ct = self.coupling_terms.get(category, None)
if ct is None:
self.coupling_terms[category] = ct = MultiCouplingTerms(self.lat.N_sites)
elif not isinstance(ct, MultiCouplingTerms):
self.coupling_terms[category] = new_ct = MultiCouplingTerms(self.lat.N_sites)
new_ct += ct
ct = new_ct
ct.add_multi_coupling_term(strength, ijkl, ops_ijkl, op_string)
[docs]class CouplingMPOModel(CouplingModel, MPOModel):
"""Combination of the :class:`CouplingModel` and :class:`MPOModel`.
This class provides the interface for most of the model classes in `tenpy`.
Examples based on this class are given in :mod:`~tenpy.models.xxz_chain`
and :mod:`~tenpy.models.tf_ising`.
The ``__init__`` of this function performs the standard initialization explained
in :doc:`/intro_model`, by calling the methods :meth:`init_lattice` (step 1-4)
to initialize a lattice (which in turn calls :meth:`init_sites`) and
:meth:`init_terms`. The latter should be overwritten by subclasses to add the
desired terms.
As shown in :mod:`~tenpy.models.tf_ising`, you can get a 1D version suitable
for TEBD from a general-lattice model by subclassing it once more, only
redefining the ``__init__`` as follows::
def __init__(self, model_params):
CouplingMPOModel.__init__(self, model_params)
Parameters
----------
model_params : dict
A dictionary with all the model parameters.
These parameters are given to the different ``init_...()`` methods, and
should be read out using :func:`~tenpy.tools.params.get_parameter`.
This may happen in any of the ``init_...()`` methods.
The parameter ``'verbose'`` is read out in the `__init__` of this function
and specifies how much status information should be printed during initialization.
The parameter ``'sort_mpo_legs'`` specifies whether the virtual legs of the MPO should be
sorted by charges (see :meth:`~tenpy.networks.mpo.MPO.sort_legcharges`).
Attributes
----------
name : str
The name of the model, e.g. ``"XXZChain" or ``"SpinModel"``.
verbose : int
Level of verbosity (i.e. how much status information to print); higher=more output.
"""
def __init__(self, model_params):
if getattr(self, "_called_CouplingMPOModel_init", False):
# If we ignore this, the same terms get added to self multiple times.
# In the best case, this would just rescale the energy;
# in the worst case we get the wrong Hamiltonian.
raise ValueError("Called CouplingMPOModel.__init__(...) multiple times.")
# To fix this problem, follow the instructions for subclassing in :doc:`/intro_model`.
self._called_CouplingMPOModel_init = True
self.name = self.__class__.__name__
self.verbose = get_parameter(model_params, 'verbose', 1, self.name)
# 1-4) iniitalize lattice
lat = self.init_lattice(model_params)
# 5) initialize CouplingModel
CouplingModel.__init__(self, lat)
# 6) add terms of the Hamiltonian
self.init_terms(model_params)
# 7) initialize H_MPO
H_MPO = self.calc_H_MPO()
if get_parameter(model_params, 'sort_mpo_legs', False, self.name):
H_MPO.sort_legcharges()
MPOModel.__init__(self, lat, H_MPO)
if isinstance(self, NearestNeighborModel):
# 8) initialize H_bonds
NearestNeighborModel.__init__(self, lat, self.calc_H_bond())
# checks for misspelled parameters
unused_parameters(model_params, self.name)
[docs] def init_lattice(self, model_params):
"""Initialize a lattice for the given model parameters.
This function reads out the model parameter `lattice`.
This can be a full :class:`~tenpy.models.lattice.Lattice` instance,
in which case it is just returned without further action.
Alternatively, the `lattice` parameter can be a string giving the name
of one of the predefined lattices, which then gets initialized.
Depending on the dimensionality of the lattice, this requires different model parameters.
The following model parameters get read out.
============== ========= ===============================================================
key type description
============== ========= ===============================================================
lattice str | The name of a lattice pre-defined in TeNPy to be initialized.
Lattice Alternatively, a (possibly self-defined) Lattice instance.
In the latter case, no further parameters are read out.
-------------- --------- ---------------------------------------------------------------
bc_MPS str Boundary conditions for the MPS
-------------- --------- ---------------------------------------------------------------
order str The order of sites within the lattice for non-trivial lattices.
-------------- --------- ---------------------------------------------------------------
L int The length in x-direction (or lenght of the unit cell for
infinite systems).
Only read out for 1D lattices.
-------------- --------- ---------------------------------------------------------------
Lx, Ly int The length in x- and y-direction.
For ``"infinite"`` `bc_MPS`, the system is infinite in
x-direction and `Lx` is the number of "rings" in the infinite
MPS unit cell, while `Ly` gives the circumference around the
cylinder or width of th the rung for a ladder (depending on
`bc_y`.
Only read out for 2D lattices.
-------------- --------- ---------------------------------------------------------------
bc_y str ``"cylinder" | "ladder"``.
The boundary conditions in y-direction.
Only read out for 2D lattices.
-------------- --------- ---------------------------------------------------------------
bc_x str ``"open" | "periodic"``.
Can be used to force "periodic" boundaries for the lattice,
i.e., for the couplings in the Hamiltonian,
even if the MPS is finite.
Defaults to ``"open"`` for ``bc_MPS="finite"`` and
``"periodic"`` for ``bc_MPS="infinite``.
If you are not aware of the consequences, you should probably
*not* use "periodic" boundary conditions.
(The MPS is still "open", so this will introduce long-range
couplings between the first and last sites of the MPS!)
============== ========= ===============================================================
Parameters
----------
model_params : dict
The model parameters given to ``__init__``.
Returns
-------
lat : :class:`~tenpy.models.lattice.Lattice`
An initialized lattice.
"""
lat = get_parameter(model_params, 'lattice', "Chain", self.name)
if isinstance(lat, str):
LatticeClass = get_lattice(lattice_name=lat)
bc_MPS = get_parameter(model_params, 'bc_MPS', 'finite', self.name)
order = get_parameter(model_params, 'order', 'default', self.name)
sites = self.init_sites(model_params)
bc_x = 'periodic' if bc_MPS == 'infinite' else 'open'
bc_x = get_parameter(model_params, 'bc_x', bc_x, self.name)
if bc_MPS == 'infinite' and bc_x == 'open':
raise ValueError("You need to use 'periodic' `bc_x` for infinite systems!")
if LatticeClass.dim == 1: # 1D lattice
L = get_parameter(model_params, 'L', 2, self.name)
# 4) lattice
lat = LatticeClass(L, sites, bc=bc_x, bc_MPS=bc_MPS)
elif LatticeClass.dim == 2: # 2D lattice
Lx = get_parameter(model_params, 'Lx', 1, self.name)
Ly = get_parameter(model_params, 'Ly', 4, self.name)
bc_y = get_parameter(model_params, 'bc_y', 'cylinder', self.name)
assert bc_y in ['cylinder', 'ladder']
bc_y = 'periodic' if bc_y == 'cylinder' else 'open'
lat = LatticeClass(Lx, Ly, sites, order=order, bc=[bc_x, bc_y], bc_MPS=bc_MPS)
else:
raise ValueError("Can't auto-determine parameters for the lattice. "
"Overwrite the `init_lattice` in your model!")
# now, `lat` is an instance of the LatticeClass called `lattice_name`.
# else: a lattice was already provided
assert isinstance(lat, Lattice)
return lat
[docs] def init_sites(self, model_params):
"""Define the local Hilbert space and operators; needs to be implemented in subclasses.
This function gets called by :meth:`init_lattice` to get the
:class:`~tenpy.networks.site.Site` for the lattice unit cell.
.. note ::
Initializing the sites requires to define the conserved quantum numbers.
All pre-defined sites accept ``conserve=None`` to disable using quantum numbers.
Many models in TeNPy read out the `conserve` model parameter, which can be set
to ``"best"`` to indicate the optimal parameters.
Parameters
----------
model_params : dict
The model parameters given to ``__init__``.
Returns
-------
sites : (tuple of) :class:`~tenpy.networks.site.Site`
The local sites of the lattice, defining the local basis states and operators.
"""
raise NotImplementedError("Subclasses should implement `init_sites`")
# or at least redefine the lattice
[docs] def init_terms(self, model_params):
"""Add the onsite and coupling terms to the model; subclasses should implement this."""
pass # Do nothing. This allows to super().init_terms(model_params) in subclasses.