# SingleSiteDMRGEngine¶

Inheritance Diagram

Methods

 SingleSiteDMRGEngine.__init__(psi, model, …) Initialize self. SingleSiteDMRGEngine.diag(theta_guess) Diagonalize the effective Hamiltonian represented by self. Perform N_sweeps sweeps without optimization to update the environment. Define the schedule of the sweep. (Re-)initialize the environment. SingleSiteDMRGEngine.mixed_svd(theta, next_B) Get (truncated) B from the new theta (as returned by diag). Set self.mixer to the class specified by engine_params[‘mixer’]. Cleanup the effects of a mixer. Plot sweep_stats to display the convergence with the sweeps. Plot update_stats to display the convergence during the sweeps. Perform post-update actions. Transform theta into matrix for svd. Prepare self to represent the effective Hamiltonian on site i0. Reset the statistics, useful if you want to start a new sweep run. Run the DMRG simulation to find the ground state. SingleSiteDMRGEngine.set_B(U, S, VH) Update the MPS with the U, S, VH returned by self.mixed_svd. SingleSiteDMRGEngine.sweep([optimize, …]) One ‘sweep’ of a sweeper algorithm. Update left part of the environment. Update right part of the environment. SingleSiteDMRGEngine.update_local(theta[, …]) Perform site-update on the site i0.
class tenpy.algorithms.dmrg.SingleSiteDMRGEngine(psi, model, engine_params)[source]

‘Engine’ for the single-site DMRG 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.

• engine_params (dict) – Further optional parameters. These are usually algorithm-specific, and thus should be described in subclasses.

EffectiveH

Class for the effective Hamiltonian (i.e., a subclass of EffectiveH. Has a length class attribute which specifies the number of sites updated at once (e.g., whether we do single-site vs. two-site DMRG).

Type

class type

chi_list

A dictionary to gradually increase the chi_max parameter of trunc_params. The key defines starting from which sweep chi_max is set to the value, e.g. {0: 50, 20: 100} uses chi_max=50 for the first 20 sweeps and chi_max=100 afterwards. Overwrites trunc_params[‘chi_list’]. By default (None) this feature is disabled.

Type

dict | None

eff_H

Effective two-site Hamiltonian.

Type

EffectiveH

mixer

If None, no mixer is used (anymore), otherwise the mixer instance.

Type

Mixer | None

shelve

If a simulation runs out of time (time.time() - start_time > max_seconds), the run will terminate with shelve = True.

Type

bool

sweeps

The number of sweeps already performed. (Useful for re-start).

Type

int

time0

Time marker for the start of the run.

Type

float

update_stats

A dictionary with detailed statistics of the convergence. For each key in the following table, the dictionary contains a list where one value is added each time Engine.update_bond() is called.

key

description

i0

An update was performed on sites i0, i0+1.

age

The number of physical sites involved in the simulation.

E_total

The total energy before truncation.

N_lanczos

Dimension of the Krylov space used in the lanczos diagonalization.

time

Wallclock time evolved since time0 (in seconds).

Type

dict

sweep_stats

A dictionary with detailed statistics of the convergence. For each key in the following table, the dictionary contains a list where one value is added each time Engine.sweep() is called (with optimize=True).

key

description

sweep

Number of sweeps performed so far.

E

The energy before truncation (as calculated by Lanczos).

S

Maximum entanglement entropy.

time

Wallclock time evolved since time0 (in seconds).

max_trunc_err

The maximum truncation error in the last sweep

max_E_trunc

Maximum change or Energy due to truncation in the last sweep.

max_chi

Maximum bond dimension used.

norm_err

Error of canonical form np.linalg.norm(psi.norm_test()).

Type

dict

prepare_update()[source]

Prepare self to represent the effective Hamiltonian on site i0.

Returns

theta – Current best guess for the ground state, which is to be optimized. Labels 'vL', 'p0', 'vR', or combined versions of it (if self.combine).

Return type

Array

update_local(theta, optimize=True, meas_E_trunc=False)[source]

Perform site-update on the site i0.

Parameters
• theta (Array) – Initial guess for the ground state of the effective Hamiltonian.

• optimize (bool) – Wheter we actually optimize to find the ground state of the effective Hamiltonian. (If False, just update the environments).

• meas_E_trunc (bool) – Wheter to measure the energy after truncation.

Returns

update_data – Data computed during the local update, as described in the following:

E0float

Total energy, obtained before truncation (if optimize=True), or after truncation (if optimize=False) (but never None).

Nint

Dimension of the Krylov space used for optimization in the lanczos algorithm. 0 if optimize=False.

ageint

Current size of the DMRG simulation: number of physical sites involved into the contraction.

U, VH: Array

U and VH returned by mixed_svd().

ov_change: float

Change in the wave function 1. - abs(<theta_guess|theta>) induced by diag(), not including the truncation!

Return type

dict

prepare_svd(theta)[source]

Transform theta into matrix for svd.

In contrast with the 2-site engine, the matrix here depends on the direction we move, as we need ‘p’ to point away from the direction we are going in.

mixed_svd(theta, next_B)[source]

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

The goal is to split theta and truncate it. For a move to the right:

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


For a move to the left:

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


The VH for right-move or U for left-move is absorebed into the next_B.

Without a mixer, this is done by a simple svd and truncation of Schmidt values of theta followed by the absorption of VH/U.

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

Parameters
Returns

• U (Array) – Left-canonical part of theta. Labels '(vL.p0)', 'vR'.

• S (1D ndarray | 2D Array) – Without mixer just the singluar 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', '(p0.vR)'.

• err (TruncationError) – The truncation error introduced.

set_B(U, S, VH)[source]

Update the MPS with the U, S, VH returned by self.mixed_svd.

Parameters
• VH (U,) – Left and Right-canonical matrices as returned by the SVD.

• S (1D array | 2D Array) – The middle part returned by the SVD, theta = U S VH. Without a mixer just the singular values, with enabled mixer a 2D array.

mixer_activate()[source]

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

update_LP(U)[source]

Update left part of the environment.

The site at which to update the environment depends on the direction of the sweep. If we are sweeping right, update the invironment at i0+1. If we are sweeping left, update the environment at i0

Parameters

U (Array) – The U as returned by SVD, with combined legs, labels '(vL.p0)', 'vR' if self.move_right, else 'vL', '(p0.vR)'.

update_RP(VH)[source]

Update right part of the environment.

The site at which to update the environment depends on the direction of the sweep. If we are sweeping right, update the invironment at i0. If we are sweeping left, update the environment at i0-1

Parameters

VH (Array) – The VH as returned by SVD, with combined legs, labels '(vL.p0)', 'vR' if self.move_right, else 'vL', '(p0.vR)'.

diag(theta_guess)[source]

Diagonalize the effective Hamiltonian represented by self.

The method used depends on the DMRG parameter diag_method.

diag_method

Function, comment

‘default’

Same as 'lanczos' for large bond dimensions, but if the total dimension of the effective Hamiltonian does not exceed the DMRG parameter 'max_N_for_ED' it uses 'ED_block'.

‘lanczos’

lanczos() Default, the Lanczos implementation in TeNPy.

‘arpack’

lanczos_arpack() Based on scipy.linalg.sparse.eigsh(). Slower than ‘lanczos’, since it needs to convert the npc arrays to numpy arrays during each matvec, and possibly does many more iterations.

‘ED_block’

full_diag_effH() Contract the effective Hamiltonian to a (large!) matrix and diagonalize the block in the charge sector of the initial state. Preserves the charge sector of the explicitly conserved charges. However, if you don’t preserve a charge explicitly, it can break it. For example if you use a SpinChain({'conserve': 'parity'}), it could change the total “Sz”, but not the parity of ‘Sz’.

‘ED_all’

full_diag_effH() Contract the effective Hamiltonian to a (large!) matrix and diagonalize it completely. Allows to change the charge sector even for explicitly conserved charges. For example if you use a SpinChain({'conserve': 'Sz'}), it can change the total “Sz”.

Parameters

theta_guess (Array) – Initial guess for the ground state of the effective Hamiltonian.

Returns

• E0 (float) – Energy of the found ground state.

• theta (Array) – Ground state of the effective Hamiltonian.

• N (int) – Number of Lanczos iterations used. -1 if unknown.

• ov_change (float) – Change in the wave function 1. - abs(<theta_guess|theta_diag>)

environment_sweeps(N_sweeps)[source]

Perform N_sweeps sweeps without optimization to update the environment.

Parameters

N_sweeps (int) – Number of sweeps to run without optimization

get_sweep_schedule()[source]

Define the schedule of the sweep.

One ‘sweep’ is a full sequence from the leftmost site to the right and back. Only those LP and RP that can be used later should be updated.

Returns

schedule – Schedule for the sweep. Each entry is (i0, move_right, (update_LP, update_RP)), where i0 is the leftmost of the self.EffectiveH.length sites to be updated in update_local(), move_right indicates whether the next i0 in the schedule is rigth (True) of the current one, and update_LP, update_RP indicate whether it is necessary to update the LP and RP. The latter are chosen such that the environment is growing for infinite systems, but we only keep the minimal number of environment tensors in memory.

Return type

iterable of (int, bool, (bool, bool))

init_env(model=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.

Raises

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

mixer_cleanup()[source]

Cleanup the effects of a mixer.

A sweep() with an enabled Mixer leaves the MPS psi with 2D arrays in S. To recover the originial form, this function simply performs one sweep with disabled mixer.

plot_sweep_stats(axes=None, xaxis='time', yaxis='E', y_exact=None, **kwargs)[source]

Plot sweep_stats to display the convergence with the sweeps.

Parameters
plot_update_stats(axes, xaxis='time', yaxis='E', y_exact=None, **kwargs)[source]

Plot update_stats to display the convergence during the sweeps.

Parameters
post_update_local(update_data, meas_E_trunc=False)[source]

Perform post-update actions.

Compute truncation energy, remove LP/RP that are no longer needed and collect statistics.

Parameters
• update_data (dict) – Data computed during the local update, as described in the following list.

• meas_E_trunc (bool, optional) – Wheter to measure the energy after truncation.

reset_stats()[source]

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

run()[source]

Run the DMRG 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 simluation, i.e. just a reference to psi.

sweep(optimize=True, meas_E_trunc=False)[source]

One ‘sweep’ of a sweeper algorithm.

Iteratate over the bond which is optimized, to the right and then back to the left to the starting point. If optimize=False, don’t actually diagonalize the effective hamiltonian, but only update the environment.

Parameters
• optimize (bool, optional) – Whether we actually optimize to find the ground state of the effective Hamiltonian. (If False, just update the environments).

• meas_E_trunc (bool, optional) – Whether to measure truncation energies.

Returns

• max_trunc_err (float) – Maximal truncation error introduced.

• max_E_trunc (None | float) – None` if meas_E_trunc is False, else the maximal change of the energy due to the truncation.