# TimeDependentExpMPOEvolution¶

Inheritance Diagram Methods

 `TimeDependentExpMPOEvolution.__init__`(psi, ...) Calculate `self._U_MPO`. `TimeDependentExpMPOEvolution.evolve`(N_steps, dt) Evolve by N_steps*dt. `TimeDependentExpMPOEvolution.evolve_step`(dt) Return necessary data to resume a `run()` interrupted at a checkpoint. Prepare an evolution step. Re-initialize a new `model` at current `evolved_time`. Resume a run that was interrupted. Perform a (real-)time evolution of `psi` by N_steps * dt. Run the time evolution for N_steps * dt. Initialize algorithm from another algorithm instance of a different class.

Class Attributes and Properties

 `TimeDependentExpMPOEvolution.time_dependent_H` whether the algorithm supports time-dependent H `TimeDependentExpMPOEvolution.verbose`
class tenpy.algorithms.mpo_evolution.TimeDependentExpMPOEvolution(psi, model, options, **kwargs)[source]

Variant of `ExpMPOEvolution` that can handle time-dependent hamiltonians.

See details in `TimeDependentHAlgorithm` as well.

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

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.

reinit_model()[source]

Re-initialize a new `model` at current `evolved_time`.

Skips re-initialization if the `model.options['time']` is the same as evolved_time. The model should read out the option `'time'` and initialize the corresponding `H(t)`.

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]

Run the time evolution for N_steps * dt.

Updates the model after each time step dt to account for changing H(t). 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 transferred. 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 = True

whether the algorithm supports time-dependent H