TimeDependentTEBD¶

full name: tenpy.algorithms.tebd.TimeDependentTEBD
parent module: tenpy.algorithms.tebd
type: class

Inheritance Diagram

Methods

`TimeDependentTEBD.__init__`(psi, model, ...)
`TimeDependentTEBD.calc_U`(order, delta_t[, ...])	Calculate `self.U_bond` from `self.model.H_bond`.
`TimeDependentTEBD.evolve`(N_steps, dt)	Evolve by `dt * N_steps`.
`TimeDependentTEBD.evolve_step`(U_idx_dt, odd)	Updates either even or odd bonds in unit cell.
`TimeDependentTEBD.get_resume_data`([...])	Return necessary data to resume a `run()` interrupted at a checkpoint.
`TimeDependentTEBD.prepare_evolve`(dt)	Prepare an evolution step.
`TimeDependentTEBD.reinit_model`()	Re-initialize a new `model` at current `evolved_time`.
`TimeDependentTEBD.resume_run`()	Resume a run that was interrupted.
`TimeDependentTEBD.run`()	Perform a (real-)time evolution of `psi` by N_steps * dt.
`TimeDependentTEBD.run_GS`()	TEBD algorithm in imaginary time to find the ground state.
`TimeDependentTEBD.run_evolution`(N_steps, dt)	Run the time evolution for N_steps * dt.
`TimeDependentTEBD.suzuki_trotter_decomposition`(...)	Returns list of necessary steps for the suzuki trotter decomposition.
`TimeDependentTEBD.suzuki_trotter_time_steps`(order)	Return time steps of U for the Suzuki Trotter decomposition of desired order.
`TimeDependentTEBD.switch_engine`(other_engine, *)	Initialize algorithm from another algorithm instance of a different class.
`TimeDependentTEBD.update_bond`(i, U_bond)	Updates the B matrices on a given bond.
`TimeDependentTEBD.update_bond_imag`(i, U_bond)	Update a bond with a (possibly non-unitary) U_bond.
`TimeDependentTEBD.update_imag`(N_steps)	Perform an update suitable for imaginary time evolution.

Class Attributes and Properties

`TimeDependentTEBD.TEBD_params`
`TimeDependentTEBD.time_dependent_H`	whether the algorithm supports time-dependent H
`TimeDependentTEBD.trunc_err_bonds`	truncation error introduced on each non-trivial bond.
`TimeDependentTEBD.verbose`

class tenpy.algorithms.tebd.TimeDependentTEBD(psi, model, options, **kwargs)[source]¶

Bases: TimeDependentHAlgorithm, TEBDEngine

Variant of TEBDEngine that can handle time-dependent Hamiltonians.

See details in TimeDependentHAlgorithm as well.

calc_U(order, delta_t, type_evo='real', E_offset=None)[source]¶

Calculate self.U_bond from self.model.H_bond.

This function calculates

U_bond = exp(-i dt (H_bond-E_offset_bond)) for type_evo='real', or
U_bond = exp(- dt H_bond) for type_evo='imag'.

For first order (in delta_t), we need just one dt=delta_t. Higher order requires smaller dt steps, as given by suzuki_trotter_time_steps().

Parameters

order (int) – Trotter order calculated U_bond. See update for more information.
delta_t (float) – Size of the time-step used in calculating U_bond
type_evo ('imag' | 'real') – Determines whether we perform real or imaginary time-evolution.
E_offset (None | list of float) – Possible offset added to H_bond for real-time evolution.

evolve(N_steps, dt)[source]¶

Evolve by dt * N_steps.

Parameters

N_steps (int) – The number of steps for which the whole lattice should be updated.
dt (float) – The time step; but really this was already used in prepare_evolve().

Returns

trunc_err – The error of the represented state which is introduced due to the truncation during this sequence of evolvution steps.

Return type

TruncationError

evolve_step(U_idx_dt, odd)[source]¶

Updates either even or odd bonds in unit cell.

Depending on the choice of p, this function updates all even (E, odd=False,0) or odd (O) (odd=True,1) bonds:

|     - B0 - B1 - B2 - B3 - B4 - B5 - B6 -
|       |    |    |    |    |    |    |
|       |    |----|    |----|    |----|
|       |    |  E |    |  E |    |  E |
|       |    |----|    |----|    |----|
|       |----|    |----|    |----|    |
|       |  O |    |  O |    |  O |    |
|       |----|    |----|    |----|    |

Note that finite boundary conditions are taken care of by having Us[0] = None.

Parameters

U_idx_dt (int) – Time step index in self._U, evolve with Us[i] = self.U[U_idx_dt][i] at bond (i-1,i).
odd (bool/int) – Indication of whether to update even (odd=False,0) or even (odd=True,1) sites

Returns

trunc_err – The error of the represented state which is introduced due to the truncation during this sequence of update steps.

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_GS()[source]¶

TEBD algorithm in imaginary time to find the ground state.

Note

It is almost always more efficient (and hence advisable) to use DMRG. This algorithms can nonetheless be used quite well as a benchmark and for comparison.

option TEBDEngine.delta_tau_list: list¶: A list of floats: the timesteps to be used. Choosing a large timestep delta_tau introduces large (Trotter) errors, but a too small time step requires a lot of steps to reach exp(-tau H) --> |psi0><psi0|. Therefore, we start with fairly large time steps for a quick time evolution until convergence, and then gradually decrease the time step.

option TEBDEngine.order: int¶: Order of the Suzuki-Trotter decomposition.

option TEBDEngine.N_steps: int¶: Number of steps before measurement can be performed

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.

static suzuki_trotter_decomposition(order, N_steps)[source]¶

Returns list of necessary steps for the suzuki trotter decomposition.

We split the Hamiltonian as \(H = H_{even} + H_{odd} = H[0] + H[1]\). The Suzuki-Trotter decomposition is an approximation \(\exp(t H) \approx prod_{(j, k) \in ST} \exp(d[j] t H[k]) + O(t^{order+1 })\).

Parameters: order (1, 2, 4, '4_opt') – The desired order of the Suzuki-Trotter decomposition. Order 1 approximation is simply \(e^A a^B\). Order 2 is the “leapfrog” e^{A/2} e^B e^{A/2}. Order 4 is the fourth-order from [suzuki1991] (also referenced in [schollwoeck2011]), and '4_opt' gives the optmized version of Equ. (30a) in [barthel2020].
Returns: ST_decomposition – Indices j, k of the time-steps d = suzuki_trotter_time_step(order) and the decomposition of H. They are chosen such that a subsequent application of exp(d[j] t H[k]) to a given state |psi> yields (exp(N_steps t H[k]) + O(N_steps t^{order+1}))|psi>.
Return type: list of (int, int)

static suzuki_trotter_time_steps(order)[source]¶

Return time steps of U for the Suzuki Trotter decomposition of desired order.

See suzuki_trotter_decomposition() for details.

Parameters: order (int) – The desired order of the Suzuki-Trotter decomposition.
Returns: time_steps – We need U = exp(-i H_{even/odd} delta_t * dt) for the dt returned in this list.
Return type: list of float

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 = True¶: whether the algorithm supports time-dependent H

property trunc_err_bonds¶: truncation error introduced on each non-trivial bond.

update_bond(i, U_bond)[source]¶

Updates the B matrices on a given bond.

Function that updates the B matrices, the bond matrix s between and the bond dimension chi for bond i. The correponding tensor networks look like this:

|           --S--B1--B2--           --B1--B2--
|                |   |                |   |
|     theta:     U_bond        C:     U_bond
|                |   |                |   |

Parameters

i (int) – Bond index; we update the matrices at sites i-1, i.
U_bond (Array) – The bond operator which we apply to the wave function. We expect labels 'p0', 'p1', 'p0*', 'p1*'.

Returns

trunc_err – The error of the represented state which is introduced by the truncation during this update step.

Return type

TruncationError

update_bond_imag(i, U_bond)[source]¶

Update a bond with a (possibly non-unitary) U_bond.

Similar as update_bond(); but after the SVD just keep the A, S, B canonical form. In that way, one can sweep left or right without using old singular values, thus preserving the canonical form during imaginary time evolution.

Parameters

i (int) – Bond index; we update the matrices at sites i-1, i.
U_bond (Array) – The bond operator which we apply to the wave function. We expect labels 'p0', 'p1', 'p0*', 'p1*'.

Returns

trunc_err – The error of the represented state which is introduced by the truncation during this update step.

Return type

TruncationError

update_imag(N_steps)[source]¶

Perform an update suitable for imaginary time evolution.

Instead of the even/odd brick structure used for ordinary TEBD, we ‘sweep’ from left to right and right to left, similar as DMRG. Thanks to that, we are actually able to preserve the canonical form.

Parameters: N_steps (int) – The number of steps for which the whole lattice should be updated.
Returns: trunc_err – The error of the represented state which is introduced due to the truncation during this sequence of update steps.
Return type: TruncationError