AKLTChain¶

full name: tenpy.models.aklt.AKLTChain
parent module: tenpy.models.aklt
type: class

Inheritance Diagram

Methods

`AKLTChain.__init__`(model_params)
`AKLTChain.bond_energies`(psi)	Calculate bond energies <psi\|H_bond\|psi>.
`AKLTChain.calc_H_MPO_from_bond`([tol_zero])	Calculate the MPO Hamiltonian from the bond Hamiltonian.
`AKLTChain.calc_H_bond_from_MPO`([tol_zero])	Calculate the bond Hamiltonian from the MPO Hamiltonian.
`AKLTChain.copy`()	Shallow copy of self.
`AKLTChain.enlarge_mps_unit_cell`([factor])	Repeat the unit cell for infinite MPS boundary conditions; in place.
`AKLTChain.extract_segment`(args, *kwargs)	Return a (shallow) copy with extracted segment of MPS.
`AKLTChain.from_MPOModel`(mpo_model)	Initialize a NearestNeighborModel from a model class defining an MPO.
`AKLTChain.from_hdf5`(hdf5_loader, h5gr, subpath)	Load instance from a HDF5 file.
`AKLTChain.group_sites`([n, grouped_sites])	Modify self in place to group sites.
`AKLTChain.save_hdf5`(hdf5_saver, h5gr, subpath)	Export self into a HDF5 file.
`AKLTChain.test_sanity`()
`AKLTChain.trivial_like_NNModel`()	Return a NearestNeighborModel with same lattice, but trivial (H=0) bonds.

Class Attributes and Properties

AKLTChain.logger

class attribute.

class tenpy.models.aklt.AKLTChain(model_params)[source]¶

Bases: tenpy.models.model.NearestNeighborModel, tenpy.models.model.MPOModel

A simple implementation of the AKLT model.

Here we define the Hamiltonian on a chain of S=1 spins as originally defined by Affleck, Kennedy, Lieb, Tasaki in [affleck1987], but dropping the constant parts of 1/3 per bond and rescaling with a factor of 2, such that we expect a ground state energy of E_0 = - (L-1) 2/3 * J.

\[H = J \sum_i 2* P^{S=2}_{i,i+1} + const = J \sum_i (\vec{S}_i \cdot \vec{S}_{i+1} +\frac{1}{3} (\vec{S}_i \cdot \vec{S}_{i+1})^2)\]

bond_energies(psi)[source]¶

Calculate bond energies <psi|H_bond|psi>.

Parameters: psi (MPS) – The MPS for which the bond energies should be calculated.
Returns: E_bond – 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.
Return type: 1D ndarray

calc_H_MPO_from_bond(tol_zero=1e-15)[source]¶

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 – MPO representation of the Hamiltonian.
Return type: MPO

calc_H_bond_from_MPO(tol_zero=1e-15)[source]¶

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 – Bond terms as required by the constructor of NearestNeighborModel. Legs are ['p0', 'p0*', 'p1', 'p1*']
Return type: list of Array

:raises ValueError : if the Hamiltonian contains longer-range terms.:

copy()[source]¶: Shallow copy of self.

enlarge_mps_unit_cell(factor=2)[source]¶

Repeat the unit cell for infinite MPS boundary conditions; in place.

This has to be done after finishing initialization and can not be reverted.

Parameters: factor (int) – The new number of sites in the MPS unit cell will be increased from N_sites to factor*N_sites_per_ring. Since MPS unit cells are repeated in the x-direction in our convetion, the lattice shape goes from (Lx, Ly, ..., Lu) to (Lx*factor, Ly, ..., Lu).

extract_segment(*args, **kwargs)[source]¶

Return a (shallow) copy with extracted segment of MPS.

Parameters

first (int) – See extract_segment().
last (int) – See extract_segment().
enlarge (int) – See extract_segment().

Returns

cp – A shallow copy of self with MPO and lattice extracted for the segment.

Return type

Model

classmethod from_MPOModel(mpo_model)[source]¶

Initialize a NearestNeighborModel from a model class defining an MPO.

This is especially usefull in combination with MPOModel.group_sites().

Parameters: mpo_model (MPOModel) – A model instance implementing the MPO. Does not need to be a 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})
>>> 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.

>>> grouped_sites = 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)
>>> isinstance(nnn_chain_for_tebd, NearestNeighborModel)
True

classmethod from_hdf5(hdf5_loader, h5gr, subpath)[source]¶

Load instance from a HDF5 file.

This method reconstructs a class instance from the data saved with save_hdf5().

Parameters

hdf5_loader (Hdf5Loader) – Instance of the loading engine.
h5gr (Group) – HDF5 group which is represent the object to be constructed.
subpath (str) – The name of h5gr with a '/' in the end.

Returns

obj – Newly generated class instance containing the required data.

Return type

cls

group_sites(n=2, grouped_sites=None)[source]¶

Modify self in place to group sites.

Group each n sites together using the 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 GroupedSite) – The sites grouped together.

Returns

grouped_sites – The sites grouped together.

Return type

list of GroupedSite

save_hdf5(hdf5_saver, h5gr, subpath)[source]¶

Export self into a HDF5 file.

This method saves all the data it needs to reconstruct self with from_hdf5().

This implementation saves the content of __dict__ with save_dict_content(), storing the format under the attribute 'format'.

Parameters

hdf5_saver (Hdf5Saver) – Instance of the saving engine.
h5gr (:class`Group`) – HDF5 group which is supposed to represent self.
subpath (str) – The name of h5gr with a '/' in the end.

trivial_like_NNModel()[source]¶: Return a NearestNeighborModel with same lattice, but trivial (H=0) bonds.