# TimeDependentHAlgorithm¶

Inheritance Diagram

Methods

 TimeDependentHAlgorithm.__init__(psi, model, ...) TimeDependentHAlgorithm.evolve(N_steps, dt) Evolve by N_steps*dt. TimeDependentHAlgorithm.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. TimeDependentHAlgorithm.switch_engine(...[, ...]) Initialize algorithm from another algorithm instance of a different class.

Class Attributes and Properties

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

Time evolution under a time dependent Hamiltonian.

TimeEvolutionAlgorithm subclasses approximate the evolution by many small time steps of dt. If we have a time-dependent Hamiltonian H(t), we can to first order in dt approximate the evolution by just updating H(t) after each time step, keeping it constant during the update step, i.e., we approximate as follows:

$U(t_0, t) = T{exp(-i int_{t_0}^t ds H(s))} \approx prod_{i=0}^{N-1} exp(-i \Delta t H(t_0 + i*\Delta t)) \textrm{ where } \Delta t = (t-t_0) / N$

Note

Even if the algorithm approximation for $$exp(-i \Delta t H(t_0 + i*\Delta t))$$ might be precise to higher order in dt, the approximation of the time dependence (and hence the overall scaling of the error with dt) is only correct to first order! Yet, if the time dependence of H is weak, it might still be better to use order > 1.

Todo

This is still under development and lacks rigorous tests.

time_dependent_H = True

whether the algorithm supports time-dependent H

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.

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 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().

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).