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.estimate_RAM_saving_factor`()	Returns the expected saving factor for RAM based on charge conservation.
`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.get_extra_default_measurements`()	Get list of model-dependent extra default measurements.
`AKLTChain.group_sites`([n, grouped_sites])	Modify self in place to group sites.
`AKLTChain.psi_AKLT`()	Initialize the chi=2 MPS which is exact ground state of the AKLT model.
`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.
`AKLTChain.update_time_parameter`(new_time)	Reconstruct Hamiltonian for time-dependent models, potentially (!) in-place.

Class Attributes and Properties

`AKLTChain.logger`	class attribute.
`AKLTChain.rng`	Reproducible numpy pseudo random number generator.

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

Bases: NearestNeighborModel, 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.

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

psi_AKLT()[source]

Initialize the chi=2 MPS which is exact ground state of the AKLT model.

Returns:: psi_aklt – The AKLT groundstate
Return type:: MPS

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 convention, the lattice shape goes from (Lx, Ly, ..., Lu) to (Lx*factor, Ly, ..., Lu).

estimate_RAM_saving_factor()[source]

Returns the expected saving factor for RAM based on charge conservation.

Returns:: factor – saving factor, due to conservation
Return type:: int

Options

mem_saving_factor :: None | float: Quantizes the RAM saving, due to conservation laws, to be used by estimate_simulation_RAM(). By default it is 1/mod, or 1/4 in case of mod=1. However, for some classes this factor might be overwritten, if a better approximation is known. In the best case, the user can adjust this model parameter to enhance the estimate.

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 useful 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, 'sort_charge': True})
>>> 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.

Same as from_hdf5(), but handle rng.

get_extra_default_measurements()[source]

Get list of model-dependent extra default measurements.

Extra measurements for a Simulation, which depend on the model itself - subclasses should override this method). E.g., a MPOModel should measure the energy w.r.t. the MPO (See m_energy_MPO()). However, a NearestNeighborModel should use the function m_bond_energies(). The extra measurements are added to the default measurements in _connect_measurements().

Returns:: m_extra_default_list
Return type:: list

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

logger = <Logger tenpy.models.model.Model (WARNING)>

class attribute.

Type:: logging.Logger
Type:: An instance of a logger; see Logging and terminal output. NB

property rng

Reproducible numpy pseudo random number generator.

If you want to add randomness/disorder to your model, it is recommended use this random number generator for reproducibility of the model:

self.rng.random(size=[3, 5])

Especially for models with time-dependence, you can/will otherwise end up generating a new disordered at each time-step!

Options

random_seed :: None | int: Defaults to 123456789. Seed for numpy pseudo random number generator which can be used as e.g. self.rng.random(...).

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

Export self into a HDF5 file.

Same as save_hdf5(), but handle rng.

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

update_time_parameter(new_time)[source]

Reconstruct Hamiltonian for time-dependent models, potentially (!) in-place.

For TimeDependentHAlgorithm, we assume that the model reads out the parameter self.options['time'], and reinitialize/update the model calling this method.

Parameters:: new_time (float) – Time at which the (time-dependent) Hamiltonian should be constructed.
Returns:: updated_model – Model of the same class as self with Hamiltonian at time new_time. Note that it can just be a reference to self if modified in place, or an entirely new constructed model.
Return type:: model