ExpMPOEvolution¶

full name: tenpy.algorithms.mpo_evolution.ExpMPOEvolution
parent module: tenpy.algorithms.mpo_evolution
type: class

Inheritance Diagram

Methods

`ExpMPOEvolution.__init__`(psi, model, options)	Initialize self.
`ExpMPOEvolution.calc_U`(dt[, order, …])	Calculate `self._U_MPO`
`ExpMPOEvolution.run`()	Run the real-time evolution with the WI/WII approximation.
`ExpMPOEvolution.update`(N_steps)	Time evolve by N_steps steps.

class tenpy.algorithms.mpo_evolution.ExpMPOEvolution(psi, model, options)[source]¶

Bases: object

Time evolution of an MPS using the W_I or W_II approximation for exp(H dt).

[zaletel2015] 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

psi (MPS) – Initial state to be time evolved. Modified in place.
model (MPOModel) – The model representing the Hamiltonian which we want to time evolve psi with.
options (dict) – Further optional parameters are described in ExpMPOEvolution.

Options

config ExpMPOEvolution¶

option	summary
approximation in ExpMPOEvolution.run	Specifies which approximation is applied. The default 'II' is more precise. [...]
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 in ExpMPOEvolution.run	Time step.
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 [...]
m_temp (from ZipUpApplyMPO) in MPO.apply_zipup	bond dimension will be truncated to `m_temp * chi_max`
N_steps in ExpMPOEvolution.run	Number of time steps `dt` to evolve
N_sweeps (from VariationalCompression) in VariationalCompression	Number of sweeps to perform.
order in ExpMPOEvolution.run	Order of the algorithm. The total error scales as ``O(t*dt^order)``. [...]
orthogonal_to (from Sweep) in DMRGEngine.init_env	List of other matrix product states to orthogonalize against. [...]
start_env (from Sweep) in DMRGEngine.init_env	Number of sweeps to be performed without optimization to update [...]
start_time	Initial value for :attr:`evolved_time`.
start_trunc_err	Initial truncation error for :attr:`trunc_err`
sweep_0 (from Sweep) in Sweep.reset_stats	Number of sweeps that have already been performed.
trunc_params	Truncation parameters as described in :cfg:config:`truncate`.
trunc_weight (from ZipUpApplyMPO) in MPO.apply_zipup	reduces cut for Schmidt values to `trunc_weight * svd_min`
verbose (from Sweep) in Sweep	Level of verbosity (i.e. how much status information to print); higher=more [...]

option trunc_params: dict¶: Truncation parameters as described in truncate.

option start_time: float¶: Initial value for evolved_time.

option start_trunc_err: TruncationError¶: Initial truncation error for trunc_err

verbose¶

Type: int

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

run()[source]¶

Run the real-time evolution with the WI/WII approximation.

Options

option ExpMPOEvolution.dt: float¶: Time step.

option ExpMPOEvolution.N_steps: int¶: Number of time steps dt to evolve

option ExpMPOEvolution.approximation: 'I' or 'II'¶: Specifies which approximation is applied. The default ‘II’ is more precise. See [zaletel2015] and make_U() for more details.

option ExpMPOEvolution.order: int¶: Order of the algorithm. The total error scales as O(t*dt^order). Implemented are order = 1 and order = 2.

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) – 1 or 2
approximation ('I' or 'II') – Type of approximation for the time evolution operator.

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