# VariationalApplyMPO¶

Inheritance Diagram

Methods

 VariationalApplyMPO.__init__(psi, U_MPO, options) Initialize self. Perform N_sweeps sweeps without optimization to update the environment. Define the schedule of the sweep. Initialize the environment. Create new instance of self.EffectiveH at self.i0 and set it to self.eff_H. Algorithm-specific actions to be taken after local update. Prepare everything algorithm-specific to perform a local update. Reset the statistics. Run the compression. VariationalApplyMPO.sweep([optimize]) One ‘sweep’ of a sweeper algorithm. VariationalApplyMPO.update_LP(_) VariationalApplyMPO.update_RP(_) VariationalApplyMPO.update_local(_[, optimize]) Perform local update. VariationalApplyMPO.update_new_psi(theta)

Class Attributes and Properties

 VariationalApplyMPO.engine_params
class tenpy.algorithms.mps_common.VariationalApplyMPO(psi, U_MPO, options)[source]

Variational compression for applying an MPO to an MPS (in place).

To apply an MPO U_MPO to an MPS psi, use VariationalApplyMPO(psi, U_MPO, options).run().

The goal is to find a new MPS phi (with N tensors) which is optimally close to U_MPO|psi>, i.e. it is normalized and maximizes | <phi|U_MPO|psi> |^2. The network for this (with M tensors for psi) is given by

.——-M[0]—-M[1]—-M[2]—- … —-.
| | | | |
LP[0]—W[0]—-W[1]—-W[2]—- … — RP[-1]
| | | | |
.——-N[0]*—N[1]*—N[2]*— … —-.

Here LP and RP are the environments with partial contractions, see also MPOEnvironment. This algorithms sweeps through the sites, updating 2 N tensors in each update_local(), say on sites i0 and i1 = i0 +1. We need to maximize:

|     .-------M[i0]---M[i1]---.
|     |       |       |       |
|     LP[i0]--W[i0]---W[i1]---RP[i1]
|     |       |       |       |
|     .-------N[i0]*--N[i1]*--.


The optimal solution is given by:

|                                     .-------M[i0]---M[i1]---.
|   ---N[i0]---N[i1]---               |       |       |       |
|      |       |          = SVD of    LP[i0]--W[i0]---W[i1]---RP[i1]
|                                     |       |       |       |
|                                     .-----                --.

Parameters

Options

config VariationalApplyMPO
option summary

combine (from Sweep) in Sweep

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

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 [...]

N_sweeps (from VariationalCompression) in VariationalCompression

Number of sweeps to perform.

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 [...]

sweep_0 (from Sweep) in Sweep.reset_stats

Number of sweeps that have already been performed.

trunc_params (from VariationalCompression) in VariationalCompression

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

verbose (from Sweep) in Sweep

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

renormalize

Used to keep track of renormalization in the last sweep for psi.norm.

Type

list

init_env(U_MPO)[source]

Initialize the environment.

Parameters

U_MPO (MPO) – The MPO to be applied to the sate.

update_local(_, optimize=True)[source]

Perform local update.

This simply contracts the environments and theta from the ket to get an updated theta for the bra self.psi (to be changed in place).

EffectiveH[source]

alias of TwoSiteH

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))

make_eff_H()[source]

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

post_update_local(update_data)[source]

Algorithm-specific actions to be taken after local update.

An example would be to collect statistics.

prepare_update()[source]

Prepare everything algorithm-specific to perform a local update.

reset_stats()[source]

Reset the statistics. Useful if you want to start a new Sweep run.

This method is expected to be overwritten by subclass, and should then define self.update_stats and self.sweep_stats dicts consistent with the statistics generated by the algorithm particular to that subclass.

option Sweep.sweep_0: int

Number of sweeps that have already been performed.

run()[source]

Run the compression.

The state psi is compressed in place.

Returns

max_trunc_err – The maximal truncation error of a two-site wave function.

Return type

TruncationError

sweep(optimize=True)[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).

Returns

max_trunc_err – Maximal truncation error introduced.

Return type

float