# ExpMPOEvolution¶

Inheritance Diagram

Methods

 ExpMPOEvolution.__init__(psi, model, ...) ExpMPOEvolution.calc_U(dt[, order, ...]) Calculate self._U_MPO. ExpMPOEvolution.evolve(N_steps, dt) Evolve by N_steps*dt. ExpMPOEvolution.evolve_step(dt) Return necessary data to resume a run() interrupted at a checkpoint. Prepare an evolution step. Resume a run that was interrupted. Perform a (real-)time evolution of psi by N_steps * dt. ExpMPOEvolution.run_evolution(N_steps, dt) Perform a (real-)time evolution of psi by N_steps * dt. ExpMPOEvolution.switch_engine(other_engine, *) Initialize algorithm from another algorithm instance of a different class.

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

max_sweeps (from VariationalCompression) in VariationalCompression

Minimum and maximum number of sweeps to perform for the compression.

min_sweeps (from VariationalCompression) in VariationalCompression

Minimum and maximum number of sweeps to perform for the compression.

N_steps (from TimeEvolutionAlgorithm) in TimeEvolutionAlgorithm

Number of time steps dt to evolve by in :meth:run. [...]

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 [...]

preserve_norm (from TimeEvolutionAlgorithm) in TimeEvolutionAlgorithm

Whether the state will be normalized to its initial norm after each time step.

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

tol_theta_diff (from VariationalCompression) in VariationalCompression

Stop after less than max_sweeps sweeps if the 1-site wave function change [...]

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

prepare_evolve(dt)[source]

Prepare an evolution step.

This method is used to prepare repeated calls of evolve() given the model. For example, it may generate approximations of U=exp(-i H dt). To avoid overhead, it may cache the result depending on parameters/options; but it should always regenerate it if force_prepare_evolve is set.

Parameters

dt (float) – The time step to be used.

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.

evolve(N_steps, dt)[source]

Evolve by N_steps*dt.

Subclasses may override this with a more efficient way of do N_steps update_step.

Parameters
• N_steps (int) – The number of time steps by dt to take at once.

• dt (float) – Small time step. Might be ignored if already used in prepare_update().

Returns

trunc_err – Sum of truncation errors introduced during evolution.

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().

run()[source]

Perform a (real-)time evolution of psi by N_steps * dt.

You probably want to call this in a loop along with measurements. The recommended way to do this is via the RealTimeEvolution.

run_evolution(N_steps, dt)[source]

Perform a (real-)time evolution of psi by N_steps * dt.

This is the inner part of run() without the logging. For parameters see TimeEvolutionAlgorithm.

classmethod switch_engine(other_engine, *, options=None, **kwargs)[source]

Initialize algorithm from another algorithm instance of a different class.

You can initialize one engine from another, not too different subclasses. Internally, this function calls get_resume_data() to extract data from the other_engine and then initializes the new class.

Note that it transfers the data without making copies in most case; even the options! Thus, when you call run() on one of the two algorithm instances, it will modify the state, environment, etc. in the other. We recommend to make the switch as engine = OtherSubClass.switch_engine(engine) directly replacing the reference.

Parameters
• cls (class) – Subclass of Algorithm to be initialized.

• other_engine (Algorithm) – The engine from which data should be transfered. Another, but not too different algorithm subclass-class; e.g. you can switch from the TwoSiteDMRGEngine to the OneSiteDMRGEngine.

• options (None | dict-like) – If not None, these options are used for the new initialization. If None, take the options from the other_engine.

• **kwargs – Further keyword arguments for class initialization. If not defined, resume_data is collected with get_resume_data()`.

time_dependent_H = False

whether the algorithm supports time-dependent H