# TimeDependentExpMPOEvolution¶

Inheritance Diagram Methods

 `TimeDependentExpMPOEvolution.__init__`(psi, ...) Calculate `self._U_MPO`. Return necessary data to resume a `run()` interrupted at a checkpoint. Re-initialize a new model at current time. Resume a run that was interrupted. Run the real-time evolution with the W_I/W_II approximation. Time evolve by N_steps steps.

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.

As of now, it only supports first `ExpMPOEvolution.order` with a very basic implementation, that just reinitializes the model after each time evolution steps with an updated model parameter time set to `evolved_time`. The model class should read that parameter.

Todo

This is still under development and lacks rigorous tests.

run()[source]

Run the real-time evolution with the W_I/W_II approximation.

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`

calc_U(dt, order, approximation)[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.

reinit_model()[source]

Re-initialize a new model at current time.

Returns

New instance of the model initialized at `model_params['time'] = self.evolved_time`.

Return type

model

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()`.