2.2. tnpy.finite_dmrg.ShiftInvertDMRG#

class tnpy.finite_dmrg.ShiftInvertDMRG(mpo, bond_dim, offset=0, block_size=1, mps=None, exact_solver_dim=200)[source]#

Bases: tnpy.finite_dmrg.FiniteDMRG

The DMRG algorithm for optimizing the shift-invert spectrum of a finite size system.

\[(H - \epsilon) \phi_n = \frac{1}{E_n - \epsilon}(H - \epsilon)^2 \phi_n\]

the original eigenvectors then can be restored through

\[\psi_n = (H - \epsilon) \phi_n\]
Parameters
__init__(mpo, bond_dim, offset=0, block_size=1, mps=None, exact_solver_dim=200)[source]#

The DMRG algorithm for optimizing the shift-invert spectrum of a finite size system.

\[(H - \epsilon) \phi_n = \frac{1}{E_n - \epsilon}(H - \epsilon)^2 \phi_n\]

the original eigenvectors then can be restored through

\[\psi_n = (H - \epsilon) \phi_n\]
Parameters

Methods

__init__(mpo, bond_dim[, offset, ...])

The DMRG algorithm for optimizing the shift-invert spectrum 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

restored_mps

__init__(mpo, bond_dim, offset=0, block_size=1, mps=None, exact_solver_dim=200)[source]#

The DMRG algorithm for optimizing the shift-invert spectrum of a finite size system.

\[(H - \epsilon) \phi_n = \frac{1}{E_n - \epsilon}(H - \epsilon)^2 \phi_n\]

the original eigenvectors then can be restored through

\[\psi_n = (H - \epsilon) \phi_n\]
Parameters
property restored_mps: tnpy.matrix_product_state.MatrixProductState | None#
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:

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-07, 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#
variance()[source]#
Return type

float