Mixer

• full name: tenpy.algorithms.dmrg.Mixer

• parent module: tenpy.algorithms.dmrg

• type: class

Inheritance Diagram

Methods

Mixer.__init__(options, sweep_activated)
Mixer.perturb_svd(engine, theta, i0, ...)	Perturb the wave function and perform an SVD with truncation.
Mixer.update_amplitude(sweeps)	Update the amplitude, possibly disable the mixer.

Class Attributes and Properties

Mixer.update_sites

how many sites the theta in perturb_svd should have

class tenpy.algorithms.dmrg.Mixer(options, sweep_activated)

Bases: object

Base class of a general Mixer.

Since DMRG performs only local updates of the state, it can get stuck in “local minima”, in particular if the Hamiltonian is long-range – which is the case if one maps a 2D system (“infinite cylinder”) to 1D – or if one wants to do single-site updates. The idea of the mixer is to perturb the state with the terms of the Hamiltonian which have contributions in both the “left” and “right” side of the system. In that way, it adds fluctuation of the quantum numbers and non-zero contributions of the long-range terms - leading to a significantly improved convergence of DMRG.

The strength of the perturbation is given by the amplitude of the mixer. A good strategy is to choose an initially significant amplitude and let it decay until the perturbation becomes completely irrelevant and the mixer gets disabled.

This original idea of the mixer was introduced in [white2005], implemented as DensityMatrixMixer. More recently, [hubig2015] discussed the mixer and provided an improved version based on an svd, which turns out to give the same results up to numerical errors; it’s implemented as the SubspaceExpansion.

Parameters

• options (dict) – Optional parameters as described in the following table. see Mixer

• sweep_activated (int) – The first sweep where the mixer was activated; disable_after is relative to that.

Options

config Mixer

option	summary
amplitude	Initial strength of the mixer. (Should be sufficiently smaller than 1.)
decay	To slowly turn off the mixer, we divide `amplitude` by `decay` [...]
disable_after	We disable the mixer completely after this number of sweeps.

option amplitude: float

Initial strength of the mixer. (Should be sufficiently smaller than 1.)

option decay: float

To slowly turn off the mixer, we divide amplitude by decay after each sweep. (Should be >= 1.)

option disable_after: int

We disable the mixer completely after this number of sweeps.

amplitude

Current amplitude for mixing. Singular values are perturbed on that order of magnitude.

Type

float

decay

Factor by which amplitude is divided after each sweep.

Type

float

disable_after

The number of sweeps after which the mixer should be disabled, relative to disable_after. Note that DMRG might repeatedly activate the mixer if you gradually increase chi with a :cfg:configoption`DMRGEngine.chi_list`.

Type

int

update_sites = 2

how many sites the theta in perturb_svd should have

update_amplitude(sweeps)

Update the amplitude, possibly disable the mixer.

Parameters

sweeps (int) – The number of performed sweeps, to check if we need to disable the mixer.

Returns

mixer – Returns self if we should continue mixing, or None, if the mixer should be disabled.

Return type

Mixer | None

perturb_svd(engine, theta, i0, update_LP, update_RP)

Perturb the wave function and perform an SVD with truncation.

The call structure is slightly different depending on update_sites; see SubspaceExpansion.perturb_svd() and DensityMatrixMixer.perturb_svd().