tensornetwork.FiniteMPS¶

class tensornetwork.FiniteMPS(tensors: List[Any], center_position: Optional[int] = None, canonicalize: Optional[bool] = True, backend: Union[str, tensornetwork.backends.abstract_backend.AbstractBackend, None] = None)¶

An MPS class for finite systems.

MPS tensors are stored as a list. FiniteMPS has a central site, also called orthogonality center. The position of this central site is stored in FiniteMPS.center_position, and it can be be shifted using the FiniteMPS.position method. FiniteMPS.position uses QR and RQ methods to shift center_position.

FiniteMPS can be initialized either from a list of tensors, or by calling the classmethod FiniteMPS.random.

By default, FiniteMPS is initialized in canonical form, i.e. the state is normalized, and all tensors to the left of center_position are left orthogonal, and all tensors to the right of center_position are right orthogonal. The tensor at FiniteMPS.center_position is neither left nor right orthogonal.

Note that canonicalization can be computationally relatively costly and scales \(\propto ND^3\).

__init__(tensors: List[Any], center_position: Optional[int] = None, canonicalize: Optional[bool] = True, backend: Union[str, tensornetwork.backends.abstract_backend.AbstractBackend, None] = None) → None¶

Initialize a FiniteMPS. If canonicalize is True the state: is brought into canonical form, with BaseMPS.center_position at center_position. if center_position is None and canonicalize = True, BaseMPS.center_position is set to 0.

Parameters:	tensors – A list of `Tensor` objects. center_position – The initial position of the center site. canonicalize – If `True` the mps is canonicalized at initialization. backend – The name of the backend that should be used to perform contractions. Available backends are currently ‘numpy’, ‘tensorflow’, ‘pytorch’, ‘jax’

Methods

`__init__`(tensors, center_position, …)	Initialize a `FiniteMPS`. If `canonicalize` is `True` the state
`apply_one_site_gate`(gate, site)	Apply a one-site gate to an MPS.
`apply_transfer_operator`(site, direction, …)	Compute the action of the MPS transfer-operator at site `site`.
`apply_two_site_gate`(gate, site1, site2, …)	Apply a two-site gate to an MPS.
`canonicalize`(normalize)	Bring the MPS into canonical form according to `center_position`.
`check_canonical`()	Check whether the MPS is in the expected canonical form.
`check_orthonormality`(which, site)	Check orthonormality of tensor at site `site`.
`get_tensor`(site)	Returns the `Tensor` object at `site`.
`left_envs`(sites)	Compute left reduced density matrices for site `sites`.
`measure_local_operator`(ops, sites)	Measure the expectation value of local operators `ops` site `sites`.
`measure_two_body_correlator`(op1, op2, site1, …)	Compute the correlator \(\langle\) `op1[site1], op2[s]`\(\rangle\) between `site1` and all sites `s` in `sites2`.
`position`(site, normalize, D, max_truncation_err)	Shift `center_position` to `site`.
`random`(d, D, dtype, canonicalize, backend, …)	Initialize a random `FiniteMPS`.
`right_envs`(sites)	Compute right reduced density matrices for site sites.This returns a dict `right_envs mapping sites (int) to Tensors.
`save`(path)

Attributes

`bond_dimensions`	A list of bond dimensions of `BaseMPS`
`dtype`
`physical_dimensions`	A list of physical Hilbert-space dimensions of `BaseMPS`

canonicalize(normalize: bool = True) → numpy.number¶

Bring the MPS into canonical form according to center_position. If center_position is None, the MPS is canonicalized with center_position = 0.

Parameters:	normalize – If `True`, normalize matrices when shifting the orthogonality center.
Returns:	The norm of the MPS.
Return type:	`Tensor`

check_canonical() → Any¶

Check whether the MPS is in the expected canonical form.

Returns:	The L2 norm of the vector of local deviations.

left_envs(sites: Sequence[int]) → Dict[KT, VT]¶

Compute left reduced density matrices for site sites. This returns a dict left_envs mapping sites (int) to Tensors. left_envs[site] is the left-reduced density matrix to the left of site site.

Parameters:	sites (list of int) – A list of sites of the MPS.
Returns:	The left-reduced density matrices at each site in `sites`.
Return type:	`dict` mapping `int` to `Tensor`

classmethod random(d: List[int], D: List[int], dtype: Type[numpy.number], canonicalize: bool = True, backend: Union[str, tensornetwork.backends.abstract_backend.AbstractBackend, None] = None) → tensornetwork.matrixproductstates.finite_mps.FiniteMPS¶

Initialize a random FiniteMPS. The resulting state is normalized. Its center-position is at 0.

Parameters:	d – A list of physical dimensions. D – A list of bond dimensions. dtype – A numpy dtype. backend – An optional backend.
Returns:	`FiniteMPS`

right_envs(sites: Sequence[int]) → Dict[KT, VT]¶

Compute right reduced density matrices for site sites. This returns a dict `right_envs mapping sites (int) to Tensors. right_envs[site] is the right-reduced density matrix to the right of site site.

Parameters:	sites (list of int) – A list of sites of the MPS.
Returns:	The right-reduced density matrices at each site in `sites`.
Return type:	`dict` mapping `int` to `Tensor`