ExactDiag

• full name: tenpy.algorithms.exact_diag.ExactDiag

• parent module: tenpy.algorithms.exact_diag

• type: class

Inheritance Diagram

Methods

ExactDiag.__init__(model[, charge_sector, ...])
ExactDiag.build_full_H_from_bonds()	Calculate self.full_H from self.mpo.
ExactDiag.build_full_H_from_mpo()	Calculate self.full_H from self.mpo.
ExactDiag.exp_H(dt)	Return U(dt) := exp(-i H dt).
ExactDiag.from_H_mpo(H_MPO, *args, **kwargs)	Wrapper taking directly an MPO instead of a Model.
ExactDiag.from_infinite_model(model[, ...])	Initialize by extracting a finite segment from a bc_MPS=infinite' model.
ExactDiag.full_diagonalization(*args, **kwargs)	Full diagonalization to obtain all eigenvalues and eigenvectors.
ExactDiag.full_to_mps(psi[, canonical_form])	Convert a full state (with a single leg) to an MPS.
ExactDiag.groundstate([charge_sector])	Pick the ground state energy and ground state from self.V.
ExactDiag.matvec(psi)	Allow to use self as LinearOperator for lanczos.
ExactDiag.mps_to_full(mps)	Contract an MPS along the virtual bonds and combine its legs.
ExactDiag.possible_charge_sectors()
ExactDiag.sparse_diag(k, *args, **kwargs)	Call speigs().

class tenpy.algorithms.exact_diag.ExactDiag(model, charge_sector=None, sparse=False, max_size=2000000.0)

Bases: object

(Full) exact diagonalization of the Hamiltonian.

Parameters

• model (MPOmodel | CouplingModel) – The model which is to be diagonalized.

• charge_sector (None | charges) – If not None, project onto the given charge sector.

• sparse (bool) – If True, don’t sort/bunch the LegPipe used to combine the physical legs. This results in array blocks with just one entry, requires much more charge data, and is not what np_conserved was designed for, so it’s not recommended.

• max_size (int) – The build_H_* functions will do nothing (but emit a warning) if the total size of the Hamiltonian would be larger than this.

model

The model which is to be diagonalized.

Type

MPOmodel | CouplingModel

chinfo

The nature of the charge (which is the same for all sites).

Type

ChargeInfo

charge_sector

If not None, we project onto the given charge sector.

Type

None | charges

max_size

The build_H_* functions will do nothing (but emit a warning) if the total size of the Hamiltonian would be larger than this.

Type

int

full_H

The full Hamiltonian to be diagonalized with legs '(p0.p1....)', '(p0*,p1*...)' (in that order). None if the build_H_* functions haven’t been called yet, or if max_size would have been exceeded.

Type

Array | None

E

1D array of eigenvalues.

Type

ndarray | None

V

Eigenvectors. First leg ‘ps’ are physical legs, the second leg 'ps*' corresponds to the eigenvalues.

Type

Array | None

_sites

The sites in the given order.

Type

list of Site

_labels_p

The labels use for the physical legs; just ['p0', 'p1', ...., 'p{L-1}'].

Type

list or str

_labels_pconj

Just each of _labels_p with an *.

Type

list or str

_pipe

The pipe from the single physical legs to the full combined leg.

Type

LegPipe

_pipe_conj

Just _pipe.conj().

Type

LegPipe

_mask

Bool mask, which of the indices of the pipe are in the desired charge_sector.

Type

1D bool ndarray | None

classmethod from_infinite_model(model, first=0, last=None, enlarge=None, **kwargs)

Initialize by extracting a finite segment from a bc_MPS=infinite' model.

This method calls extract_segment() on the model and sets the boundary conditions to ‘finite’. For the ExactDiag, this little hack is equivalent to extracting all the coupling terms fitting within the segment specified by first, last and None, and generating a finite MPOModel from it.

Note that it drops the H_bond if existent, since build_full_H_from_bonds() would not include the correct, full onsite-terms at the boundaries if just drop the H_bond going outside the segment. Hence you can only use the build_full_H_from_mpo() method when initializing the ExactDiag with this method.

Parameters

model (tenpy.models.model.Model) – Model with infinite bc and MPO.

classmethod from_H_mpo(H_MPO, *args, **kwargs)

Wrapper taking directly an MPO instead of a Model.

Parameters

• H_MPO (MPO) – The MPO representing the Hamiltonian.

• *args – Further keyword arguments as for the __init__ of the class.

• **kwargs – Further keyword arguments as for the __init__ of the class.

build_full_H_from_mpo()

Calculate self.full_H from self.mpo.

build_full_H_from_bonds()

Calculate self.full_H from self.mpo.

full_diagonalization(*args, **kwargs)

Full diagonalization to obtain all eigenvalues and eigenvectors.

Arguments are given to eigh.

groundstate(charge_sector=None)

Pick the ground state energy and ground state from self.V.

Parameters

charge_sector (None | 1D ndarray) – By default (None), consider all charge sectors. Alternatively, give the qtotal which the returned state should have.

Returns

• E0 (float) – Ground state energy (possibly in the given sector).

• psi0 (Array) – Ground state (possibly in the given sector).

exp_H(dt)

Return U(dt) := exp(-i H dt).

mps_to_full(mps)

Contract an MPS along the virtual bonds and combine its legs.

Parameters

mps (MPS) – The MPS to be contracted.

Returns

psi – The MPS contracted along the virtual bonds.

Return type

Array

full_to_mps(psi, canonical_form='B')

Convert a full state (with a single leg) to an MPS.

Parameters

• psi (Array) – The state (with a single leg) which should be splitted into an MPS.

• canonical_from (Array) – The form in which the MPS will be afterwards.

Returns

mps – An normalized MPS representation in canonical form.

Return type

MPS

matvec(psi)

Allow to use self as LinearOperator for lanczos.

Just applies full_H to (the first axis of) the given psi.

sparse_diag(k, *args, **kwargs)

Call speigs().