ExpMPOEvolution¶

full name: tenpy.algorithms.mpo_evolution.ExpMPOEvolution
parent module: tenpy.algorithms.mpo_evolution
type: class

Inheritance Diagram

Methods

`ExpMPOEvolution.__init__`(psi, model, ...)
`ExpMPOEvolution.calc_U`(dt[, order, ...])	Calculate `self._U_MPO`.
`ExpMPOEvolution.get_resume_data`([...])	Return necessary data to resume a `run()` interrupted at a checkpoint.
`ExpMPOEvolution.resume_run`()	Resume a run that was interrupted.
`ExpMPOEvolution.run`()	Run the real-time evolution with the W_I/W_II approximation.
`ExpMPOEvolution.update`(N_steps)	Time evolve by N_steps steps.

Class Attributes and Properties

`ExpMPOEvolution.time_dependent_H`	whether the algorithm supports time-dependent H
`ExpMPOEvolution.verbose`

class tenpy.algorithms.mpo_evolution.ExpMPOEvolution(psi, model, options, **kwargs)[source]¶

Bases: tenpy.algorithms.algorithm.TimeEvolutionAlgorithm

Time evolution of an MPS using the W_I or W_II approximation for exp(H dt).

[zaletel2015] described a method to obtain MPO approximations \(W_I\) and \(W_{II}\) for the exponential U = exp(i H dt) of an MPO H, implemented in make_U_I() and make_U_II(). This class uses it for real-time evolution.

Parameters are the same as for Algorithm.

Options

config ExpMPOEvolution¶

option	summary
approximation	Specifies which approximation is applied. The default 'II' is more precise. [...]
chi_list (from Sweep) in Sweep.reset_stats	By default (``None``) this feature is disabled. [...]
combine (from Sweep) in Sweep	Whether to combine legs into pipes. This combines the virtual and [...]
compression_method (from ApplyMPO) in MPO.apply	Mandatory. [...]
dt (from TimeEvolutionAlgorithm) in TimeEvolutionAlgorithm	Minimal time step by which to evolve.
init_env_data (from Sweep) in DMRGEngine.init_env	Dictionary as returned by ``self.env.get_initialization_data()`` from [...]
lanczos_params (from Sweep) in Sweep	Lanczos parameters as described in :cfg:config:`Lanczos`.
m_temp (from ZipUpApplyMPO) in MPO.apply_zipup	bond dimension will be truncated to `m_temp * chi_max`
N_steps (from TimeEvolutionAlgorithm) in TimeEvolutionAlgorithm	Number of time steps `dt` to evolve by in :meth:`run`. [...]
N_sweeps (from VariationalCompression) in VariationalCompression	Number of sweeps to perform.
order	Order of the algorithm. The total error up to time `t` scales as ``O(t*dt^o [...]
orthogonal_to (from Sweep) in DMRGEngine.init_env	Deprecated in favor of the `orthogonal_to` function argument (forwarded fro [...]
start_env (from Sweep) in DMRGEngine.init_env	Number of sweeps to be performed without optimization to update the environment.
start_env_sites (from VariationalCompression) in VariationalCompression	Number of sites to contract for the inital LP/RP environment in case of inf [...]
start_time (from TimeEvolutionAlgorithm) in TimeEvolutionAlgorithm	Initial value for :attr:`evolved_time`.
start_trunc_err	Initial truncation error for :attr:`trunc_err`
trunc_params (from ApplyMPO) in MPO.apply	Truncation parameters as described in :cfg:config:`truncation`.
trunc_weight (from ZipUpApplyMPO) in MPO.apply_zipup	reduces cut for Schmidt values to `trunc_weight * svd_min`

option start_trunc_err: TruncationError¶: Initial truncation error for trunc_err

option approximation: 'I' | 'II'¶: Specifies which approximation is applied. The default ‘II’ is more precise. See [zaletel2015] and make_U() for more details.

option order: int¶: Order of the algorithm. The total error up to time t scales as O(t*dt^order). Implemented are order = 1 and order = 2.

options¶

Optional parameters, see run() for more details

Type: Config

evolved_time¶

Indicating how long psi has been evolved, psi = exp(-i * evolved_time * H) psi(t=0).

Type: float

trunc_err¶

The error of the represented state which is introduced due to the truncation during the sequence of update steps

Type: TruncationError

psi¶

The MPS, time evolved in-place.

Type: MPS

model¶

The model defining the Hamiltonian.

Type: MPOModel

_U¶

Exponentiated H_MPO;

Type: list of MPO

_U_param¶

A dictionary containing the information of the latest created _U. We won’t recalculate _U if those parameters didn’t change.

Type: dict

run()[source]¶: Run the real-time evolution with the W_I/W_II approximation.

calc_U(dt, order=2, approximation='II')[source]¶

Calculate self._U_MPO.

This function calculates the approximation U ~= exp(-i dt_ H) with dt_ = dt` for ``order=1, or dt_ = (1 - 1j)/2 dt and dt_ = (1 + 1j)/2 dt for order=2.

Parameters

dt (float) – Size of the time-step used in calculating _U
order (int) – The order of the algorithm. Only 1 and 2 are allowed.
approximation ('I' or 'II') – Type of approximation for the time evolution operator.

update(N_steps)[source]¶

Time evolve by N_steps steps.

Parameters: N_steps (int) – The number of time steps psi is evolved by.
Returns: trunc_err – Truncation error induced during the update.
Return type: TruncationError

get_resume_data(sequential_simulations=False)[source]¶

Return necessary data to resume a run() interrupted at a checkpoint.

At a checkpoint, you can save psi, model and options along with the data returned by this function. When the simulation aborts, you can resume it using this saved data with:

eng = AlgorithmClass(psi, model, options, resume_data=resume_data)
eng.resume_run()

An algorithm which doesn’t support this should override resume_run to raise an Error.

Parameters: sequential_simulations (bool) – If True, return only the data for re-initializing a sequential simulation run, where we “adiabatically” follow the evolution of a ground state (for variational algorithms), or do series of quenches (for time evolution algorithms); see run_seq_simulations().
Returns: resume_data – Dictionary with necessary data (apart from copies of psi, model, options) that allows to continue the simulation from where we are now. It might contain an explicit copy of psi.
Return type: dict

resume_run()[source]¶

Resume a run that was interrupted.

In case we saved an intermediate result at a checkpoint, this function allows to resume the run() of the algorithm (after re-initialization with the resume_data). Since most algorithms just have a while loop with break conditions, the default behaviour implemented here is to just call run().