MPOGraph

• full name: tenpy.networks.mpo.MPOGraph

• parent module: tenpy.networks.mpo

• type: class

Inheritance Diagram

Methods

MPOGraph.__init__(sites[, bc, max_range, ...])
MPOGraph.add(i, keyL, keyR, opname, strength)	Insert an edge into the graph.
MPOGraph.add_missing_IdL_IdR([insert_all_id])	Add missing identity ('Id') edges connecting 'IdL'->'IdL' and ``'IdR'->'IdR'.
MPOGraph.add_string_left_to_right(i, j, key)	Insert a bunch of edges for an 'operator string' into the graph.
MPOGraph.add_string_right_to_left(j, i, key)	Insert a bunch of edges for an 'operator string' into the graph.
MPOGraph.build_MPO([Ws_qtotal])	Build the MPO represented by the graph (self).
MPOGraph.from_term_list(term_list, sites, bc)	Initialize from a list of operator terms and prefactors.
MPOGraph.from_terms(terms, sites, bc[, ...])	Initialize an MPOGraph from OnsiteTerms and CouplingTerms.
MPOGraph.get_site(i)	Get the i-th site.
MPOGraph.has_edge(i, keyL, keyR)	True if there is an edge from keyL on bond (i-1, i) to keyR on bond (i, i+1).
MPOGraph.shift_Array_unit_cells(arr, ...[, ...])	Shift an Array by an integer multiple of unit cells.
MPOGraph.shift_Site_unit_cells(site, ...)	Shift a site by an integer multiple of unit cells.
MPOGraph.shift_charges_unit_cells(charges, ...)	Shift charges by an integer multiple of unit cells.
MPOGraph.test_sanity()	Sanity check, raises ValueErrors, if something is wrong.

Class Attributes and Properties

MPOGraph.L	Number of physical sites; for an iMPS the len of the MPS unit cell.
MPOGraph.N_sites_per_hor_spacing	Number of sites per horizontal lattice spacing.
MPOGraph.dim	List of local physical dimensions.
MPOGraph.finite	Distinguish MPS vs iMPS.
MPOGraph.nontrivial_bonds	Slice of the non-trivial bond indices, depending on self.bc.

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

Bases: MPSGeometry

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 virtual 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 ‘identity 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:

• sites (list of Site) – Local sites of the Hilbert space.

• bc ({'finite', 'infinite'}) – MPO boundary conditions.

• max_range (int | np.inf | None) – Maximum range of hopping/interactions (in unit of sites) of the MPO. None for unknown.

• unit_cell_width (int) – See num_unit_cell_width.

max_range

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

Type:

int | np.inf | None

states

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

Type:

list of set of keys

graph

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

Type:

list of dict of dict of list of tuples

_grid_legs

The charges for the MPO

Type:

None | list of LegCharge

classmethod from_terms(terms, sites, bc, insert_all_id=True, unit_cell_width=None)

Initialize an MPOGraph from OnsiteTerms and CouplingTerms.

Parameters:

• terms (iterable of tenpy.networks.terms.*Terms classes) – Entries can be OnsiteTerms, CouplingTerms, MultiCouplingTerms or ExponentialCouplingTerms. All the entries get added to the new MPOGraph.

• sites (list of Site) – Local sites of the Hilbert space.

• bc ('finite' | 'infinite') – MPO boundary conditions.

• insert_all_id (bool) – Whether to insert identities such that IdL and IdR are defined on each bond. See add_missing_IdL_IdR().

• unit_cell_width (int) – See mps_unit_cell_width.

Returns:

graph – Initialized with the given terms.

Return type:

MPOGraph

See also

from_term_list

equivalent for representation by TermList.

classmethod from_term_list(term_list, sites, bc, insert_all_id=True, unit_cell_width=None)

Initialize from a list of operator terms and prefactors.

Parameters:

• term_list (TermList) – Terms to be added to the MPOGraph.

• sites (list of Site) – Local sites of the Hilbert space.

• bc ('finite' | 'infinite') – MPO boundary conditions.

• insert_all_id (bool) – Whether to insert identities such that IdL and IdR are defined on each bond. See add_missing_IdL_IdR().

• unit_cell_width (int) – See mps_unit_cell_width.

Returns:

graph – Initialized with the given terms.

Return type:

MPOGraph

See also

from_terms

equivalent for other representation of terms.

test_sanity()

Sanity check, raises ValueErrors, if something is wrong.

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

Insert an edge into the graph.

Parameters:

• i (int) – Site index at which the edge of the graph is to be inserted.

• keyL (hashable) – The state at bond (i-1, i) to connect from.

• keyR (hashable) – The state at bond (i, i+1) to connect to.

• opname (str) – Name of the operator.

• strength (str) – Prefactor of the operator to be inserted.

• check_op (bool) – Whether to check that ‘opname’ exists on the given site.

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

add_string_left_to_right(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 (int) – An edge is inserted on all sites 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.

• j (int) – An edge is inserted on all sites 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 (tuple) – The key at bond (i+1, i) to connect from.

• opname (str) – Name of the operator to be used for the string. Useful for the Jordan-Wigner transformation to fermions.

• skip_existing (bool) – Whether existing graph nodes should be skipped.

Returns:

key_i – The key on the right of site i we connected to.

Return type:

tuple

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

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

Similar as add_string_left_to_right(), but in the other direction.

Parameters:

• j (int) – An edge is inserted on all sites between i and j, i < j. Note the switched argument order compared to add_string_left_to_right().

• i (int) – An edge is inserted on all sites between i and j, i < j. Note the switched argument order compared to add_string_left_to_right().

• key (tuple) – The key at bond (j-1, j) to connect from.

• opname (str) – Name of the operator to be used for the string. Useful for the Jordan-Wigner transformation to fermions.

• skip_existing (bool) – Whether existing graph nodes should be skipped.

Returns:

key_i – The key on the right of site i we connected to.

Return type:

hashable

add_missing_IdL_IdR(insert_all_id=True)

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

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

Parameters:

insert_all_id (bool) – If True, insert ‘Id’ edges on all bonds. If False and boundary conditions are finite, only insert 'IdL'->'IdL' to the left of the rightmost existing ‘IdL’ and 'IdR'->'IdR' to the right of the leftmost existing ‘IdR’. The latter avoid “dead ends” in the MPO, but some functions (like make_WI) expect ‘IdL’/’IdR’ to exist on all bonds.

has_edge(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(Ws_qtotal=None)

Build the MPO represented by the graph (self).

Parameters:

• Ws_qtotal (None | (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.

• unit_cell_width (int) – See mps_unit_cell_width.

Returns:

mpo – the MPO which self represents.

Return type:

MPO

property L

Number of physical sites; for an iMPS the len of the MPS unit cell.

property N_sites_per_hor_spacing

Number of sites per horizontal lattice spacing.

This is the number of MPS sites one has to traverse to travel one lattice spacing in the first dimension, such that self.unit_cell_width * N_sites_per_hor_spacing == self.L.

property dim

List of local physical dimensions.

property finite

Distinguish MPS vs iMPS.

True for an MPS (bc='finite', 'segment'), False for an iMPS (bc='infinite').

get_site(i)

Get the i-th site.

This is self.sites[i] if i is in the unit cell and takes care of shifting the charges otherwise.

property nontrivial_bonds

Slice of the non-trivial bond indices, depending on self.bc.

shift_Array_unit_cells(arr, num_unit_cells, inplace: bool = False)

Shift an Array by an integer multiple of unit cells.

See the notes on Dipole Conservation.

A unit cell has length L and a shift by one unit cell is purely horizontal and shifts by unit_cell_width lattice spacings.

Parameters:

• arr (Array) – The site to shift.

• num_unit_cells (int) – The number of unit cells.

• inplace (bool) – If the array (its legs, qtotal) can be modified in-place. Otherwise (default) we make a shallow copy.

Returns:

The shifted array.

Return type:

Array

shift_Site_unit_cells(site, num_unit_cells)

Shift a site by an integer multiple of unit cells.

See the notes on Dipole Conservation.

A unit cell has length L and a shift by one unit cell is purely horizontal and shifts by unit_cell_width lattice spacings.

Parameters:

• site (Site) – The site to shift.

• num_unit_cells (int) – The number of unit cells.

Returns:

A new site with shifted charges, or the unmodified input site if the shift is trivial.

Return type:

Site

shift_charges_unit_cells(charges, num_unit_cells)

Shift charges by an integer multiple of unit cells.

See the notes on Dipole Conservation.

A unit cell has length L and a shift by one unit cell is purely horizontal and shifts by unit_cell_width lattice spacings.

Essentially, this is a convenience wrapper around \(tenpy.linalg.charges.ChargeInfo.shift_charges_horizontal\).

Parameters:

• charges (2D ndarray of dtype QTYPE) – The charges to shift.

• num_unit_cells (int) – The number of unit cells.

Returns:

The shifted charges.

Return type:

2D ndarray of dtype QTYPE