Mixer¶
full name: tenpy.algorithms.dmrg.Mixer
parent module:
tenpy.algorithms.dmrg
type: class
Inheritance Diagram
Methods
|
Initialize self. |
|
Perturb the wave function and perform an SVD with truncation. |
|
Update the amplitude, possibly disable the mixer. |
-
class
tenpy.algorithms.dmrg.
Mixer
(options)[source]¶ 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 Hamiltonain 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 (currently not implemented in TeNPy). 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]. [hubig2015] discusses the mixer and provides an improved version.
- Parameters
env (
MPOEnvironment
) – Environment for contraction<psi|H|psi>
for lateroptions (dict) – Optional parameters as described in the following table. see
Mixer
Options
-
config
Mixer
¶ option summary Initial strength of the mixer. (Should be << 1.)
To slowly turn off the mixer, we divide `amplitude` by `decay` [...]
We disable the mixer completely after this number of sweeps.
-
option
amplitude
: float¶ Initial strength of the mixer. (Should be << 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.
-
option
-
perturb_svd
(engine, theta, i0, update_LP, update_RP)[source]¶ Perturb the wave function and perform an SVD with truncation.
- Parameters
engine (
DMRGEngine
) – The DMRG engine calling the mixer.theta (
Array
) – The optimized wave function, prepared for svd.i0 (int) – Site index; theta lives on
i0, i0+1
.update_LP (bool) – Whether to calculate the next
env.LP[i0+1]
.update_RP (bool) – Whether to calculate the next
env.RP[i0]
.
- 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; see comment above.VH (
Array
) – Right-canonical part of theta. Labels'vL', '(vR.p1)'
.err (
TruncationError
) – The truncation error introduced.