# ExpMPOEvolution¶

Inheritance Diagram

Methods

 ExpMPOEvolution.__init__(psi, model, ...) ExpMPOEvolution.calc_U(dt[, order, ...]) Calculate self._U_MPO. Return necessary data to resume a run() interrupted at a checkpoint. Resume a run that was interrupted. 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]

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

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 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()`.