MPOGraph

• full name: tenpy.networks.mpo.MPOGraph

• parent module: tenpy.networks.mpo

• type: class

class tenpy.networks.mpo.MPOGraph(sites, bc='finite', max_range=None)

Bases: object

Representation of an MPO by a graph, based on a ‘finite state machine’.

This representation is used for building H_MPO from the interactions. The idea is to view the MPO as a kind of ‘finite state machine’. The states or keys of this finite state machine life on the MPO bonds between the Ws. They label the indices of the virtul bonds of the MPOs, i.e., the indices on legs wL and wR. They can be anything hash-able like a str, int or a tuple of them.

The edges of the graph are the entries W[keyL, keyR], which itself are onsite operators on the local Hilbert space. The indices keyL and keyR correspond to the legs 'wL', 'wR' of the MPO. The entry W[keyL, keyR] connects the state keyL on bond (i-1, i) with the state keyR on bond (i, i+1).

The keys 'IdR' (for ‘idenity left’) and 'IdR' (for ‘identity right’) are reserved to represent only 'Id' (=identity) operators to the left and right of the bond, respectively.

Todo

might be useful to add a “cleanup” function which removes operators cancelling each other and/or unused states. Or better use a ‘compress’ of the MPO?

Parameters

siteslist of Site

Local sites of the Hilbert space.

bc{‘finite’, ‘infinite’}

MPO boundary conditions.

max_rangeint | np.inf | None

Maximum range of hopping/interactions (in unit of sites) of the MPO. None for unknown.

Attributes

L

Number of physical sites; for infinite boundaries the length of the unit cell.

siteslist of Site

Defines the local Hilbert space for each site.

chinfoChargeInfo

The nature of the charge.

bc{‘finite’, ‘infinite’}

MPO boundary conditions.

max_rangeint | np.inf | None

Maximum range of hopping/interactions (in unit of sites) of the MPO. None for unknown.

stateslist of set of keys

states[i] gives the possible keys at the virtual bond (i-1, i) of the MPO.

graphlist of dict of dict of list of tuples

For each site i a dictionary {keyL: {keyR: [(opname, strength)]}} with keyL in vertices[i] and keyR in vertices[i+1].

_grid_legsNone | list of LegCharge

The charges for the MPO

Methods

add(self, i, keyL, keyR, opname, strength[, …])	Insert an edge into the graph.
add_missing_IdL_IdR(self)	Add missing identity (‘Id’) edges connecting 'IdL'->'IdL' and ``'IdR'->'IdR'.
add_string(self, i, j, key[, opname, …])	Insert a bunch of edges for an ‘operator string’ into the graph.
build_MPO(self[, Ws_qtotal, leg0])	Build the MPO represented by the graph (self).
from_term_list(term_list, sites, bc)	Initialize form a list of operator terms and prefactors.
from_terms(onsite_terms, coupling_terms, …)	Initialize an MPOGraph from OnsiteTerms and CouplingTerms.
has_edge(self, i, keyL, keyR)	True if there is an edge from keyL on bond (i-1, i) to keyR on bond (i, i+1).
test_sanity(self)	Sanity check, raises ValueErrors, if something is wrong.

classmethod from_terms(onsite_terms, coupling_terms, sites, bc)

Initialize an MPOGraph from OnsiteTerms and CouplingTerms.

Parameters

onsite_termsOnsiteTerms

Onsite terms to be added to the new MPOGraph.

coupling_terms :class:`~tenpy.networks.terms.CouplingTerms` | :class:`~tenpy.networks.terms.MultiCouplingTerms`

Coupling terms to be added to the new MPOGraph.

siteslist of Site

Local sites of the Hilbert space.

bc'finite' | 'infinite'

MPO boundary conditions.

Returns

graphMPOGraph

Initialized with the given terms.

See also

from_term_list

equivalent for other representation terms.

classmethod from_term_list(term_list, sites, bc)

Initialize form a list of operator terms and prefactors.

Parameters

term_listTermList

Terms to be added to the MPOGraph.

siteslist of Site

Local sites of the Hilbert space.

bc'finite' | 'infinite'

MPO boundary conditions.

Returns

graphMPOGraph

Initialized with the given terms.

See also

from_terms

equivalent for other representation of terms.

test_sanity(self)

Sanity check, raises ValueErrors, if something is wrong.

property L

Number of physical sites; for infinite boundaries the length of the unit cell.

add(self, i, keyL, keyR, opname, strength, check_op=True, skip_existing=False)

Insert an edge into the graph.

Parameters

iint

Site index at which the edge of the graph is to be inserted.

keyLhashable

The state at bond (i-1, i) to connect from.

keyRhashable

The state at bond (i, i+1) to connect to.

opnamestr

Name of the operator.

strengthstr

Prefactor of the operator to be inserted.

check_opbool

Whether to check that ‘opname’ exists on the given site.

skip_existingbool

If True, skip adding the graph node if it exists (with same keys and opname).

add_string(self, i, j, key, opname='Id', check_op=True, skip_existing=True)

Insert a bunch of edges for an ‘operator string’ into the graph.

Terms like \(S^z_i S^z_j\) actually stand for \(S^z_i \otimes \prod_{i < k < j} \mathbb{1}_k \otimes S^z_j\). This function adds the \(\mathbb{1}\) terms to the graph.

Parameters

i, j: int

An edge is inserted on all bonds between i and j, i < j. j can be larger than L, in which case the operators are supposed to act on different MPS unit cells.

key: hashable

The state at bond (i-1, i) to connect from and on bond (j-1, j) to connect to. Also used for the intermediate states. No operator is inserted on a site i < k < j if has_edge(k, key, key).

opnamestr

Name of the operator to be used for the string. Useful for the Jordan-Wigner transformation to fermions.

skip_existingbool

Whether existing graph nodes should be skipped.

Returns

label_jhashable

The key on the left of site j to connect to. Usually the same as the parameter key, except if j - i > self.L, in which case we use the additional labels (key, 1), (key, 2), … to generate couplings over multiple unit cells.

add_missing_IdL_IdR(self)

Add missing identity (‘Id’) edges connecting 'IdL'->'IdL' and ``'IdR'->'IdR'.

For bc='infinite', insert missing identities at all bonds. For bc='finite' | 'segment' only insert 'IdL'->'IdL' to the left of the rightmost existing ‘IdL’ and 'IdR'->'IdR' to the right of the leftmost existing ‘IdR’.

This function should be called after all other operators have been inserted.

has_edge(self, i, keyL, keyR)

True if there is an edge from keyL on bond (i-1, i) to keyR on bond (i, i+1).

build_MPO(self, Ws_qtotal=None, leg0=None)

Build the MPO represented by the graph (self).

Parameters

Ws_qtotalNone | (list of) charges

The qtotal for each of the Ws to be generated., default (None) means 0 charge. A single qtotal holds for each site.

leg0None | npc.LegCharge

The charges to be used for the very first leg (which is a gauge freedom). If None (default), use zeros.

Returns

mpoMPO

the MPO which self represents.