2.1. tnpy.finite_dmrg.FiniteDMRG#

class tnpy.finite_dmrg.FiniteDMRG(mpo, bond_dim, block_size=1, mps=None, exact_solver_dim=200)[source]#

Bases: object

The Density Matrix Renormalization Group (DMRG) algorithm of a finite size system.

Parameters

Examples

To start the algorithm, one can call run(),

>>> fdmrg = FiniteDMRG(mpo, bond_dim=20)
>>> fdmrg.run(tol=1e-8)

The optimized MatrixProductState can then be retrieved from mps.

__init__(mpo, bond_dim, block_size=1, mps=None, exact_solver_dim=200)[source]#

The Density Matrix Renormalization Group (DMRG) algorithm of a finite size system.

Parameters

Examples

To start the algorithm, one can call run(),

>>> fdmrg = FiniteDMRG(mpo, bond_dim=20)
>>> fdmrg.run(tol=1e-8)

The optimized MatrixProductState can then be retrieved from mps.

Methods

__init__(mpo, bond_dim[, block_size, mps, ...])

The Density Matrix Renormalization Group (DMRG) algorithm of a finite size system.

one_site_solver(site[, tol])

param site

perturb_wave_function(site[, alpha])

Perturb the local tensor of wave function by an amount of alpha.

run([tol, max_sweep, metric])

By calling this method, FiniteDMRG will start the sweeping procedure until the given tolerance is reached or touching the maximally allowed number of sweeps.

sweep([direction, tol])

Perform a single sweep on the given direction.

two_site_solver(site[, tol])

variance()

Attributes

bond_dim

measurements

mps

n_sites

phys_dim

__init__(mpo, bond_dim, block_size=1, mps=None, exact_solver_dim=200)[source]#

The Density Matrix Renormalization Group (DMRG) algorithm of a finite size system.

Parameters

Examples

To start the algorithm, one can call run(),

>>> fdmrg = FiniteDMRG(mpo, bond_dim=20)
>>> fdmrg.run(tol=1e-8)

The optimized MatrixProductState can then be retrieved from mps.

property bond_dim: int#
property mps: tnpy.matrix_product_state.MatrixProductState#
property n_sites: int#
property phys_dim: int#
variance()[source]#
Return type

float

one_site_solver(site, tol=1e-08, **kwargs)[source]#
Parameters

  • site (int) –

  • tol (float) – Tolerance to the eigensolver.

  • **kwargs – Keyword arguments to primme eigensolver.

Return type

Tuple[float, numpy.ndarray]

Returns:

two_site_solver(site, tol=1e-08, **kwargs)[source]#
Parameters

  • site (int) –

  • tol (float) –

perturb_wave_function(site, alpha=1e-05)[source]#

Perturb the local tensor of wave function by an amount of alpha. For the single-site DMRG one_site_solver(), the modified density matrix can be used against trapping in local minimums. This is an in-place operation.

Parameters

  • site (int) –

  • alpha (float) – The small parameter for perturbation.

References

1. S. R. White, Density matrix renormalization group algorithms with a single center site, Phys. Rev. B 72, 180403 (2005).

2. U. Schollwoeck, The density-matrix renormalization group in the age of matrix product states, arXiv:1008.3477 (2011).

sweep(direction=Direction.RIGHTWARD, tol=1e-08, **kwargs)[source]#

Perform a single sweep on the given direction.

Parameters

  • direction (tnpy.matrix_product_state.Direction) – The left or right direction on which the sweep to perform.

  • tol (float) – Tolerance to the eigensolver.

  • **kwargs – Keyword arguments to primme eigensolver.

Returns

Variationally optimized energy after this sweep.

Return type

float | None

run(tol=1e-08, max_sweep=100, metric=Metric.ENERGY, **kwargs)[source]#

By calling this method, FiniteDMRG will start the sweeping procedure until the given tolerance is reached or touching the maximally allowed number of sweeps.

Parameters

  • tol (float) – Required precision to the variationally optimized energy.

  • max_sweep (int) – Maximum number of sweeps.

  • metric (tnpy.finite_dmrg.Metric) – By which value to examine the convergence.

  • **kwargs – Keyword arguments to primme eigensolver.

Returns

A record of energies computed on each sweep.

Return type

List[float]

property measurements: tnpy.matrix_product_state.MatrixProductStateMeasurements#