# 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. Create new instance of self.EffectiveH at self.i0 and set it to self.eff_H. 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 options[‘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 for calling update_local() 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 the 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 Attributes and Properties

 SingleSiteDMRGEngine.DMRG_params SingleSiteDMRGEngine.engine_params
class tenpy.algorithms.dmrg.SingleSiteDMRGEngine(psi, model, options)[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.

• options (dict) – Further optional parameters.

Options

config SingleSiteDMRGEngine
option summary

chi_list (from DMRGEngine) in DMRGEngine.reset_stats

A dictionary to gradually increase the chi_max parameter of [...]

combine (from Sweep) in Sweep

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

diag_method (from DMRGEngine) in DMRGEngine.run

Method to be used for diagonalzation, default 'default'. [...]

E_tol_max (from DMRGEngine) in DMRGEngine.run

See E_tol_to_trunc

E_tol_min (from DMRGEngine) in DMRGEngine.run

See E_tol_to_trunc

E_tol_to_trunc (from DMRGEngine) in DMRGEngine.run

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

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 [...]

max_E_err (from DMRGEngine) in DMRGEngine.run

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

max_hours (from DMRGEngine) in DMRGEngine.run

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_S_err (from DMRGEngine) in DMRGEngine.run

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

max_sweeps (from DMRGEngine) in DMRGEngine.run

Maximum number of sweeps to be performed.

min_sweeps (from DMRGEngine) in DMRGEngine.run

Minimum number of sweeps to be performed. [...]

mixer in SingleSiteDMRGEngine.mixer_activate

Chooses the :class:Mixer to be used. [...]

mixer_params in SingleSiteDMRGEngine.mixer_activate

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

N_sweeps_check (from DMRGEngine) in DMRGEngine.run

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

norm_tol (from DMRGEngine) in DMRGEngine.run

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

norm_tol_iter (from DMRGEngine) in DMRGEngine.run

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

orthogonal_to (from Sweep) in DMRGEngine.init_env

List of other matrix product states to orthogonalize against. [...]

P_tol_max (from DMRGEngine) in DMRGEngine.run

See P_tol_to_trunc

P_tol_min (from DMRGEngine) in DMRGEngine.run

See P_tol_to_trunc

P_tol_to_trunc (from DMRGEngine) in DMRGEngine.run

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 [...]

sweep_0 (from DMRGEngine) in DMRGEngine.reset_stats

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

trunc_params (from Sweep) in Sweep

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

update_env (from DMRGEngine) in DMRGEngine.run

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

verbose (from Sweep) in Sweep

Level of verbosity (i.e. how much status information to print); higher=more [...]

EffectiveH[source]

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

EffectiveH[source]
prepare_update()[source]

Prepare self for calling update_local() 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)[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).

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 options[‘mixer’].

option SingleSiteDMRGEngine.mixer: str | class | bool

Chooses the Mixer to be used. A string stands for one of the mixers defined in this module, a class is used as custom mixer. Default (None) uses no mixer, True uses DensityMatrixMixer for the 2-site case and SingleSiteMixer for the 1-site case.

option SingleSiteDMRGEngine.mixer_params: dict

Mixer parameters as described in 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.

option DMRGEngine.max_N_for_ED: int

Maximum matrix dimension of the effective hamiltonian up to which the 'default' diag_method uses ED instead of Lanczos.

option DMRGEngine.diag_method: str

One of the folloing strings:

‘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.

Options

Deprecated since version 0.6.0: Options LP, LP_age, RP and RP_age are now collected in a dictionary init_env_data with different keys init_LP, init_RP, age_LP, age_RP

option Sweep.init_env_data: dict

Dictionary as returned by self.env.get_initialization_data() from get_initialization_data().

option Sweep.orthogonal_to: list of MPSEnvironment

List of other matrix product states to orthogonalize against. Works only for finite systems. This parameter 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.

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.

make_eff_H()[source]

Create new instance of self.EffectiveH at self.i0 and set it to self.eff_H.

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)[source]

Perform post-update actions.

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

Parameters

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

reset_stats()[source]

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

option DMRGEngine.chi_list: dict | None

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.

option DMRGEngine.sweep_0: int

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

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.

Options

option DMRGEngine.diag_method: str

Method to be used for diagonalzation, default 'default'. For possible arguments see DMRGEngine.diag().

option DMRGEngine.E_tol_to_trunc: float

It’s reasonable to choose the Lanczos convergence criteria 'E_tol' not many magnitudes lower than the current truncation error. Therefore, if E_tol_to_trunc is not None, we update E_tol of lanczos_params to max_E_trunc*E_tol_to_trunc, restricted to the interval [E_tol_min, E_tol_max], where max_E_trunc is the maximal energy difference due to truncation right after each Lanczos optimization during the sweeps.

option DMRGEngine.E_tol_max: float

See E_tol_to_trunc

option DMRGEngine.E_tol_min: float

See E_tol_to_trunc

option DMRGEngine.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 is also satisfied if Delta E > 0, i.e., if the energy increases (due to truncation).

option DMRGEngine.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.

option DMRGEngine.max_S_err: float

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

option DMRGEngine.max_sweeps: int

Maximum number of sweeps to be performed.

option DMRGEngine.min_sweeps: int

Minimum number of sweeps to be performed. Defaults to 1.5*N_sweeps_check.

option DMRGEngine.N_sweeps_check: int

Number of sweeps to perform between checking convergence criteria and giving a status update.

option DMRGEngine.norm_tol: float

After the DMRG run, update the environment with at most norm_tol_iter sweeps until np.linalg.norm(psi.norm_err()) < norm_tol.

option DMRGEngine.norm_tol_iter: float

Perform at most norm_tol_iter*update_env sweeps to converge the norm error below norm_tol. If the state is not converged after that, call canonical_form() instead.

option DMRGEngine.P_tol_to_trunc: float

It’s reasonable to choose the Lanczos convergence criteria 'P_tol' not many magnitudes lower than the current truncation error. Therefore, if P_tol_to_trunc is not None, we update P_tol of lanczos_params to max_trunc_err*P_tol_to_trunc, restricted to the interval [P_tol_min, P_tol_max], where max_trunc_err is the maximal truncation error (discarded weight of the Schmidt values) due to truncation right after each Lanczos optimization during the sweeps.

option DMRGEngine.P_tol_max: float

See P_tol_to_trunc

option DMRGEngine.P_tol_min: float

See P_tol_to_trunc

option DMRGEngine.update_env: int

Number of sweeps without bond optimizaiton to update the environment for infinite boundary conditions, performed every N_sweeps_check sweeps.

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

One ‘sweep’ of a the algorithm.

Iteratate 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 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.