TwoSiteVUMPSEngine

Inheritance Diagram

Inheritance diagram of tenpy.algorithms.vumps.TwoSiteVUMPSEngine

Methods

TwoSiteVUMPSEngine.__init__(psi, model, ...)

TwoSiteVUMPSEngine.environment_sweeps(N_sweeps)

In VUMPS we don't want to do this as we regenerate the environment each time we do an update.

TwoSiteVUMPSEngine.estimate_RAM([...])

Gives an approximate prediction for the required memory usage.

TwoSiteVUMPSEngine.free_no_longer_needed_envs()

Remove no longer needed environments after an update.

TwoSiteVUMPSEngine.get_resume_data([...])

Return necessary data to resume a run() interrupted at a checkpoint.

TwoSiteVUMPSEngine.get_sweep_schedule()

Sweep from site 0 to L-1

TwoSiteVUMPSEngine.init_env([model, ...])

(Re-)initialize the environment.

TwoSiteVUMPSEngine.is_converged()

Determines if the algorithm is converged.

TwoSiteVUMPSEngine.make_eff_H()

Create new instance of self.EffectiveH at self.i0.

TwoSiteVUMPSEngine.mixed_svd(theta)

Get (truncated) B from the new theta (as returned by diag).

TwoSiteVUMPSEngine.mixer_activate()

Set self.mixer to the class specified by options['mixer'].

TwoSiteVUMPSEngine.mixer_cleanup()

For uniform MPS there is no need to clean up after the mixer.

TwoSiteVUMPSEngine.mixer_deactivate()

Deactivate the mixer.

TwoSiteVUMPSEngine.polar_max(AC1, AC2, C1, C3)

Polar decompositions on two sites: Given AC1 and C1, find AR1 such that AC1 = C1 AR1 and from AC2 and C3, find AL2 such that AC2 = AC2 C3

TwoSiteVUMPSEngine.post_run_cleanup()

Perform any final steps or clean up after the main loop has terminated.

TwoSiteVUMPSEngine.post_update_local(e_L, ...)

Perform post-update actions.

TwoSiteVUMPSEngine.pre_run_initialize()

Perform preparations before run_iteration() is iterated.

TwoSiteVUMPSEngine.prepare_update_local()

For each update, we need to rebuild the environments from scratch using the most recent tensors

TwoSiteVUMPSEngine.reset_stats([resume_data])

Reset the statistics, useful if you want to start a new sweep run.

TwoSiteVUMPSEngine.resume_run()

Resume a run that was interrupted.

TwoSiteVUMPSEngine.run()

Run the VUMPS simulation to find the ground state.

TwoSiteVUMPSEngine.run_iteration()

Perform a single iteration, consisting of N_sweeps_check sweeps.

TwoSiteVUMPSEngine.status_update(...)

Emits a status message to the logging system after an iteration.

TwoSiteVUMPSEngine.stopping_criterion(...)

Determines if the main loop should be terminated.

TwoSiteVUMPSEngine.sweep([optimize])

One 'sweep' of a sweeper algorithm.

TwoSiteVUMPSEngine.switch_engine(other_engine, *)

Initialize algorithm from another algorithm instance of a different class.

TwoSiteVUMPSEngine.tangent_projector_test(...)

The ground state projector P_GS

TwoSiteVUMPSEngine.update_env(**update_data)

Update the left and right environments after an update of the state.

TwoSiteVUMPSEngine.update_local(theta, **kwargs)

Perform two-site update on the site i0 and i0+1.

Class Attributes and Properties

TwoSiteVUMPSEngine.S_inv_cutoff

TwoSiteVUMPSEngine.lanczos_options

Deprecated alias of lanczos_params.

TwoSiteVUMPSEngine.n_optimize

The number of sites to be optimized at once.

TwoSiteVUMPSEngine.use_mixer_by_default

class tenpy.algorithms.vumps.TwoSiteVUMPSEngine(psi, model, options, **kwargs)[source]

Bases: VUMPSEngine

Engine for the two-site VUMPS algorithm.

Parameters:
  • psi (MPS) – Initial guess for the ground state, which is to be optimized in-place.

  • model (MPOModel) – The model representing the Hamiltonian for which we want to find the ground state.

  • options (dict) – Further optional parameters.

Options

config TwoSiteDMRGEngine
option summary

chi_list (from Sweep) in IterativeSweeps.reset_stats

By default (``None``) this feature is disabled. [...]

chi_list_reactivates_mixer (from Sweep) in IterativeSweeps.sweep

If True, the mixer is reset/reactivated each time the bond dimension growth [...]

combine (from Sweep) in Sweep

Whether to combine legs into pipes. This combines the virtual and [...]

diag_method (from DMRGEngine) in DMRGEngine.diag

One of the following strings: [...]

E_tol_max (from DMRGEngine) in DMRGEngine.run_iteration

See `E_tol_to_trunc`

E_tol_min (from DMRGEngine) in DMRGEngine.run_iteration

See `E_tol_to_trunc`

E_tol_to_trunc (from DMRGEngine) in DMRGEngine.run_iteration

It's reasonable to choose the Lanczos convergence criteria [...]

lanczos_params (from Sweep) in Sweep

Lanczos parameters as described in :cfg:config:`KrylovBased`.

max_E_err (from DMRGEngine) in DMRGEngine.is_converged

Convergence if the change of the energy in each step [...]

max_hours (from IterativeSweeps) in DMRGEngine.stopping_criterion

If the DMRG took longer (measured in wall-clock time), [...]

max_N_for_ED (from DMRGEngine) in DMRGEngine.diag

Maximum matrix dimension of the effective hamiltonian [...]

max_N_sites_per_ring (from Algorithm) in Algorithm

Threshold for raising errors on too many sites per ring. Default ``18``. [...]

max_S_err (from DMRGEngine) in DMRGEngine.is_converged

Convergence if the relative change of the entropy in each step [...]

max_sweeps (from IterativeSweeps) in DMRGEngine.stopping_criterion

Maximum number of sweeps to perform.

max_trunc_err (from IterativeSweeps) in IterativeSweeps

Threshold for raising errors on too large truncation errors. Default ``0.00 [...]

min_sweeps (from IterativeSweeps) in DMRGEngine.stopping_criterion

Minimum number of sweeps to perform.

mixer (from Sweep) in DMRGEngine.mixer_activate

Specifies which :class:`Mixer` to use, if any. [...]

mixer_params (from Sweep) in DMRGEngine.mixer_activate

Mixer parameters as described in :cfg:config:`Mixer`.

N_sweeps_check (from DMRGEngine) in DMRGEngine.run_iteration

Number of sweeps to perform between checking convergence [...]

norm_tol (from DMRGEngine) in DMRGEngine.post_run_cleanup

After the DMRG run, update the environment with at most [...]

norm_tol_final (from DMRGEngine) in DMRGEngine.post_run_cleanup

After performing `norm_tol_iter`*`update_env` sweeps, if [...]

norm_tol_iter (from DMRGEngine) in DMRGEngine.post_run_cleanup

Perform at most `norm_tol_iter`*`update_env` sweeps to [...]

P_tol_max (from DMRGEngine) in DMRGEngine.run_iteration

See `P_tol_to_trunc`

P_tol_min (from DMRGEngine) in DMRGEngine.run_iteration

See `P_tol_to_trunc`

P_tol_to_trunc (from DMRGEngine) in DMRGEngine.run_iteration

It's reasonable to choose the Lanczos convergence criteria [...]

start_env (from Sweep) in DMRGEngine.init_env

Number of sweeps to be performed without optimization to update the environment.

trunc_params (from Algorithm) in Algorithm

Truncation parameters as described in :cfg:config:`truncation`.

update_env (from DMRGEngine) in DMRGEngine.run_iteration

Number of sweeps without bond optimization to update the [...]

EffectiveH[source]

alias of TwoSiteH

DefaultMixer[source]

alias of SubspaceExpansion

update_env(**update_data)[source]

Update the left and right environments after an update of the state.

Parameters:

**update_data – Whatever is returned by update_local().

update_local(theta, **kwargs)[source]

Perform two-site update on the site i0 and i0+1.

Parameters:

theta (3-tuple of Array) – Initial guesses for the ground state of the effective Hamiltonian and zero-site Hamiltonians.

Returns:

update_data – Data computed during the local update.

Return type:

dict

polar_max(AC1, AC2, C1, C3)[source]

Polar decompositions on two sites: Given AC1 and C1, find AR1 such that AC1 = C1 AR1 and from AC2 and C3, find AL2 such that AC2 = AC2 C3

Parameters:
  • AC1 (Array) – Center-site tensor at site i0

  • AC2 (Array) – Center-site tensor at site i0+1

  • C1 (Array) – Center matrix left of site i0

  • C3 (Array) – Center matrix right of site i0+1

Returns:

  • AL2 (Array) – Left-orthonormal tensor such that AL2 C3 = AC2

  • AR1 (Array) – Right-orthonormal tensor such that C1 AR1 = AC1

  • eps_L (float) – Norm error, || AC1 - AL2 C3 ||

  • eps_R (float) – Norm error, || AC2 - C1 AR1 ||

  • entropy_left (float) – entanglement entropy left of site i0

  • entropy_right (float) – entanglement entropy right of site i0+1

mixed_svd(theta)[source]

Get (truncated) B from the new theta (as returned by diag).

The goal is to split theta and truncate it:

|   -- theta --   ==>    -- U -- S --  VH -
|      |   |                |          |

Without a mixer, this is done by a simple svd and truncation of Schmidt values.

With a mixer, the state is perturbed before the SVD. The details of the perturbation are defined by the Mixer class.

Note that the returned S is a general (not diagonal) matrix, with labels 'vL', 'vR'.

Parameters:

theta (Array) – The optimized wave function, prepared for svd.

Returns:

  • U (Array) – Left-canonical part of theta. Labels '(vL.p)', 'vR'.

  • S (2D Array) – Without mixer just the singular values of the array; with mixer it might be a general matrix with labels 'vL', 'vR'; see comment above.

  • VH (Array) – Right-canonical part of theta. Labels 'vL', '(p.vR)'.

  • err (TruncationError) – The truncation error introduced.

  • S_approx (ndarray) – Just the S if a 1D ndarray, or an approximation of the correct S (which was used for truncation) in case S is 2D Array.

environment_sweeps(N_sweeps)[source]

In VUMPS we don’t want to do this as we regenerate the environment each time we do an update.

estimate_RAM(mem_saving_factor=None)[source]

Gives an approximate prediction for the required memory usage.

This calculation is based on the requested bond dimension, the local Hilbert space dimension, the number of sites, and the boundary conditions.

Parameters:

mem_saving_factor (float) – Represents the amount of RAM saved due to conservation laws. By default, it is ‘None’ and is extracted from the model automatically. However, this is only possible in a few cases and needs to be estimated in most cases. This is due to the fact that it is dependent on the model parameters. If one has a better estimate, one can pass the value directly. This value can be extracted by building the initial state psi (usually by performing DMRG) and then calling print(psi.get_B(0).sparse_stats()) TeNPy will automatically print the fraction of nonzero entries in the first line, for example, 6 of 16 entries (=0.375) nonzero. This fraction corresponds to the mem_saving_factor; in our example, it is 0.375.

Returns:

usage – Required RAM in MB.

Return type:

float

See also

tenpy.simulations.simulation.estimate_simulation_RAM

global function calling this.

free_no_longer_needed_envs()[source]

Remove no longer needed environments after an update.

This allows to minimize the number of environments to be kept. For large MPO bond dimensions, these environments are by far the biggest part in memory, so this is a valuable optimization to reduce memory requirements.

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 algorithm run from where we are now. It might contain an explicit copy of psi.

Return type:

dict

get_sweep_schedule()[source]

Sweep from site 0 to L-1

init_env(model=None, resume_data=None, orthogonal_to=None)[source]

(Re-)initialize the environment.

This function is useful to (re-)start a Sweep with a slightly different model or different (engine) parameters. Note that we assume that we still have the same psi. Calls reset_stats().

Parameters:
  • model (MPOModel) – The model representing the Hamiltonian for which we want to find the ground state. If None, keep the model used before.

  • resume_data (None | dict) – Given when resuming a simulation, as returned by get_resume_data(). Can contain another dict under the key init_env_data; the contents of init_env_data get passed as keyword arguments to the environment initialization.

  • orthogonal_to (None | list of MPS | list of dict) – List of other matrix product states to orthogonalize against. Instead of just the state, you can specify a dict with the state as ket and further keyword arguments for initializing the MPSEnvironment; the psi to be optimized is used as bra. Works only for finite or segment MPS; for infinite MPS it must be None. This can be used to find (a few) excited states as follows. First, run DMRG to find the ground state, and then run DMRG again while orthogonalizing against the ground state, which yields the first excited state (in the same symmetry sector), and so on. Note that resume_data['orthogonal_to'] takes precedence over the argument.

Options

option Sweep.start_env: int

Number of sweeps to be performed without optimization to update the environment.

Raises:

ValueError – If the engine is re-initialized with a new model, which legs are incompatible with those of hte old model.

is_converged()[source]

Determines if the algorithm is converged.

Does not cover any other reasons to abort, such as reaching a time limit. Such checks are covered by stopping_condition().

Options

option VUMPSEngine.max_E_err: float

Convergence if the change of the energy in each step satisfies |Delta E / max(E, 1)| < max_E_err. Note that this might be satisfied even if Delta E > 0, i.e., if the energy increases (due to truncation).

option VUMPSEngine.max_S_err: float

Convergence if the relative change of the entropy in each step satisfies |Delta S|/S < max_S_err

option VUMPSEngine.max_split_err: float

Convergence if the norm error between AC=AL-C and AC=C_AR is smaller than max_split_err.

property lanczos_options

Deprecated alias of lanczos_params.

make_eff_H()[source]

Create new instance of self.EffectiveH at self.i0. Also create zero-site Hamiltonians left of self.i0 and right of self.i0+self.n_optimize.

mixer_activate()[source]

Set self.mixer to the class specified by options[‘mixer’].

option Sweep.mixer: str | class | bool | None

Specifies which Mixer to use, if any. A string stands for one of the mixers defined in this module. A class is assumed to have the same interface as Mixer and is used to instantiate the mixer. None uses no mixer. True uses the mixer specified by the DefaultMixer class attribute. The default depends on the subclass of Sweep.

option Sweep.mixer_params: dict

Mixer parameters as described in Mixer.

See also

mixer_deactivate

mixer_cleanup()[source]

For uniform MPS there is no need to clean up after the mixer.

mixer_deactivate()[source]

Deactivate the mixer.

Set self.mixer=None and revert any other effects of mixer_activate().

property n_optimize

The number of sites to be optimized at once.

Indirectly set by the class attribute EffectiveH and it’s length. For example, TwoSiteDMRGEngine uses the TwoSiteH and hence has n_optimize=2, while the SingleSiteDMRGEngine has n_optimize=1.

post_run_cleanup()[source]

Perform any final steps or clean up after the main loop has terminated. Try to convert uniform MPS back to iMPS.

Options

option VUMPSEngine.check_overlap: bool

Since AL C = C AR is not identically true, the MPS defined by AL and AR are not exactly the same. We can compute the overlap of the two to check.

option VUMPSEngine.norm_tol: float

Check if final state is in canonical form.

post_update_local(e_L, e_R, eps_L, eps_R, e_C1, e_C2, e_theta, N0_L, N0_R, N1, **update_data)[source]

Perform post-update actions.

Collect statistics.

Parameters:

**update_data (dict) – What was returned by update_local().

pre_run_initialize()[source]

Perform preparations before run_iteration() is iterated.

Returns:

The object to be returned by run() in case of immediate convergence, i.e. if no iterations are performed.

Return type:

result

prepare_update_local()[source]

For each update, we need to rebuild the environments from scratch using the most recent tensors

reset_stats(resume_data=None)[source]

Reset the statistics, useful if you want to start a new sweep run.

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 behavior implemented here is to just call run().

run()[source]

Run the VUMPS simulation to find the ground state.

Returns:

  • E (float) – The energy of the resulting ground state MPS.

  • psi (MPS) – The MPS representing the ground state after the simulation, i.e. just a reference to psi.

run_iteration()[source]

Perform a single iteration, consisting of N_sweeps_check sweeps.

Options

option VUMPSEngine.diagonal_gauge_frequency: int

Number of sweeps how often we restore the UniformMPS to the diagonal gauge

option VUMPSEngine.cutoff: float

During DMRG with a mixer, S may be a matrix for which we need the inverse. This is calculated as the Penrose pseudo-inverse, which uses a cutoff for the singular values.

Returns:

  • E (float) – The energy of the current ground state approximation.

  • psi (UniformMPS) – The current ground state approximation, i.e. just a reference to psi.

status_update(iteration_start_time: float)[source]

Emits a status message to the logging system after an iteration.

Parameters:

iteration_start_time (float) – The time.time() at the start of the last iteration

stopping_criterion(iteration_start_time: float) bool[source]

Determines if the main loop should be terminated.

Parameters:

iteration_start_time (float) – The time.time() at the start of the last iteration

Options

option IterativeSweeps.min_sweeps: int

Minimum number of sweeps to perform.

option IterativeSweeps.max_sweeps: int

Maximum number of sweeps to perform.

option IterativeSweeps.max_hours: float

If the DMRG took longer (measured in wall-clock time), ‘shelve’ the simulation, i.e. stop and return with the flag shelve=True.

Returns:

should_break – If True, the main loop in run() is broken.

Return type:

bool

sweep(optimize=True)[source]

One ‘sweep’ of a sweeper algorithm.

Iterate over the bond which is optimized, to the right and then back to the left to the starting point.

Parameters:

optimize (bool, optional) – Whether we actually optimize the state, e.g. to find the ground state of the effective Hamiltonian in case of a DMRG. (If False, just update the environments).

Options

option Sweep.chi_list_reactivates_mixer: bool

If True, the mixer is reset/reactivated each time the bond dimension growths due to Sweep.chi_list.

Returns:

max_trunc_err – Maximal truncation error introduced.

Return type:

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 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().

tangent_projector_test(env_data)[source]

The ground state projector P_GS