DensityMatrixMixer¶

full name: tenpy.algorithms.dmrg.DensityMatrixMixer
parent module: tenpy.algorithms.dmrg
type: class

class tenpy.algorithms.dmrg.DensityMatrixMixer(mixer_params)[source]¶

Bases: tenpy.algorithms.dmrg.Mixer

Mixer based on density matrices.

This mixer constructs density matrices as described in the original paper [White2005].

Methods

`get_xL`(self, wL_leg, Id_L, Id_R)	Generate the coupling of the MPO legs for the reduced density matrix.
`get_xR`(self, wR_leg, Id_L, Id_R)	Generate the coupling of the MPO legs for the reduced density matrix.
`mix_rho_L`(self, engine, theta, i0, mix_enabled)	Calculated mixed reduced density matrix for left site.
`mix_rho_R`(self, engine, theta, i0, mix_enabled)	Calculated mixed reduced density matrix for left site.
`perturb_svd`(self, engine, theta, i0, …)	Mix extra terms to theta and perform an SVD.
`update_amplitude`(self, sweeps)	Update the amplitude, possibly disable the mixer.

perturb_svd(self, engine, theta, i0, update_LP, update_RP)[source]¶

Mix extra terms to theta and perform an SVD.

We calculate the left and right reduced density using the mixer (which might include applications of H). These density matrices are diagonalized and truncated such that we effectively perform a svd for the case mixer.amplitude=0.

Parameters

engineSingleSiteDMRGEngine | TwoSiteDMRGEngine: The DMRG engine calling the mixer.
thetaArray: The optimized wave function, prepared for svd.
i0int: Site index; theta lives on i0, i0+1.
update_LPbool: Whether to calculate the next env.LP[i0+1].
update_RPbool: Whether to calculate the next env.RP[i0].

Returns

UArray: Left-canonical part of theta. Labels '(vL.p0)', 'vR'.
S1D ndarray | 2D Array: Without mixer just the singluar values of the array; with mixer it might be a general matrix; see comment above.
VHArray: Right-canonical part of theta. Labels 'vL', '(p1.vR)'.
errTruncationError: The truncation error introduced.

mix_rho_L(self, engine, theta, i0, mix_enabled)[source]¶

Calculated mixed reduced density matrix for left site.

Pictorially:

|     mix_enabled=False           mix_enabled=True
|
|    .---theta---.            .---theta-------.
|    |   |   |   |            |   |   |       |
|            |   |           LP---H0--H1--.   |
|    |   |   |   |            |   |   |   |   |
|    .---theta*--.                    |   xR  |
|                             |   |   |   |   |
|                            LP*--H0*-H1*-.   |
|                             |   |   |       |
|                             .---theta*------.

Parameters

engineEngine: The DMRG engine calling the mixer.
thetaArray: Ground state of the effective Hamiltonian, prepared for svd.
i0int: Site index; theta lives on i0, i0+1.
mix_enabledbool: Whether we should perturb the density matrix.

Returns

rho_LArray: A (hermitian) square array with labels '(vL.p0)', '(vL*.p0*)', Mainly the reduced density matrix of the left part, but with some additional mixing.

mix_rho_R(self, engine, theta, i0, mix_enabled)[source]¶

Calculated mixed reduced density matrix for left site.

Pictorially:

|     mix_enabled=False           mix_enabled=True
|
|    .---theta---.           .------theta---.
|    |   |   |   |           |      |   |   |
|    |   |                   |   .--H0--H1--RP
|    |   |   |   |           |   |  |   |   |
|    .---theta*--.           |  wL  |
|                            |   |  |   |   |
|                            |   .--H0*-H1*-RP*
|                            |      |   |   |
|                            .------theta*--.

Parameters

engineEngine: The DMRG engine calling the mixer.
thetaArray: Ground state of the effective Hamiltonian, prepared for svd.
i0int: Site index; theta lives on i0, i0+1.
mix_enabledbool: Whether we should perturb the density matrix.

Returns

rho_RArray: A (hermitian) square array with labels '(p1.vR)', '(p1*.vR*)'. Mainly the reduced density matrix of the right part, but with some additional mixing.

get_xR(self, wR_leg, Id_L, Id_R)[source]¶

Generate the coupling of the MPO legs for the reduced density matrix.

Parameters

wR_legLegCharge: LegCharge to be connected to.
IdLint | None: Index within the leg for which the MPO has only identities to the left.
IdRint | None: Index within the leg for which the MPO has only identities to the right.

Returns

mixed_xRArray: Connection of the MPOs on the right for the reduced density matrix rhoL. Labels ('wL', 'wL*').
add_separate_Idbool: If Id_L is None, we can’t include the identity into mixed_xR, so it has to be added directly in mix_rho_L().

get_xL(self, wL_leg, Id_L, Id_R)[source]¶

Generate the coupling of the MPO legs for the reduced density matrix.

Parameters

wL_legLegCharge: LegCharge to be connected to.
Id_Lint | None: Index within the leg for which the MPO has only identities to the left.
Id_Rint | None: Index within the leg for which the MPO has only identities to the right.

Returns

mixed_xLArray: Connection of the MPOs on the left for the reduced density matrix rhoR. Labels ('wR', 'wR*').
add_separate_Idbool: If Id_R is None, we can’t include the identity into mixed_xL, so it has to be added directly in mix_rho_R().

update_amplitude(self, sweeps)¶

Update the amplitude, possibly disable the mixer.

Parameters

sweepsint: The number of performed sweeps, to check if we need to disable the mixer.

Returns

mixerMixer | None: Returns self if we should continue mixing, or None, if the mixer should be disabled.