TwoSiteH

full name: tenpy.algorithms.mps_common.TwoSiteH
parent module: tenpy.algorithms.mps_common
type: class

Inheritance Diagram

Methods

`TwoSiteH.__init__`(env, i0[, combine, move_right])
`TwoSiteH.adjoint`()	Return the hermitian conjugate of self.
`TwoSiteH.combine_Heff`(env[, left, right])	Combine LP and RP with W to form LHeff and RHeff.
`TwoSiteH.combine_theta`(theta)	Combine the legs of theta, such that it fits to how we combined the legs of self.
`TwoSiteH.matvec`(theta)	Apply the effective Hamiltonian to theta.
`TwoSiteH.to_matrix`()	Contract self to a matrix.
`TwoSiteH.update_LP`(env, i[, U])	Equivalent to `env.get_LP(i, store=True)`; optimized for combine.
`TwoSiteH.update_RP`(env, i[, VH])	Equivalent to `env.get_RP(i, store=True)`; optimized for combine.

Class Attributes and Properties

`TwoSiteH.acts_on`
`TwoSiteH.length`

class tenpy.algorithms.mps_common.TwoSiteH(env, i0, combine=False, move_right=True)[source]

Bases: EffectiveH

Class defining the two-site effective Hamiltonian for Lanczos.

The effective two-site Hamiltonian looks like this:

|        .---       ---.
|        |    |   |    |
|       LP----W0--W1---RP
|        |    |   |    |
|        .---       ---.

If combine is True, we define LHeff and RHeff, which are the contractions of LP with W0, and RP with W1, respectively.

Parameters:

env (MPOEnvironment) – Environment for contraction <psi|H|psi>.
i0 (int) – Left-most site of the MPS it acts on.
combine (bool) – Whether to combine legs into pipes. This combines the virtual and physical leg for the left site (when moving right) or right side (when moving left) into pipes. This reduces the overhead of calculating charge combinations in the contractions, but one matvec() is formally more expensive, \(O(2 d^3 \chi^3 D)\).
move_right (bool | None) – Whether the the sweep is moving right or left for the next update (or doesn’t move). Ignored for the TwoSiteH.

i0

Left-most site of the MPS it acts on.

Type:: int

combine

Whether to combine legs into pipes. This combines the virtual and physical leg for the left site and right site into pipes. This reduces the overhead of calculating charge combinations in the contractions, but one matvec() is formally more expensive, \(O(2 d^3 \chi^3 D)\).

Type:: bool

length

Number of (MPS) sites the effective hamiltonian covers.

Type:: int

acts_on

Labels of the state on which self acts. NB: class attribute. Overwritten by normal attribute, if combine.

Type:: list of str

LHeff

Left part of the effective Hamiltonian. Labels '(vR*.p0)', 'wR', '(vR.p0*)' for bra, MPO, ket.

Type:: Array

RHeff

Right part of the effective Hamiltonian. Labels '(p1*.vL)', 'wL', '(p1.vL*)' for ket, MPO, bra.

Type:: Array

LP, W0, W1, RP

Tensors making up the network of self.

Type:: Array

matvec(theta)[source]

Apply the effective Hamiltonian to theta.

Parameters:: theta (Array) – Labels: vL, p0, p1, vR if combine=False, (vL.p0), (p1.vR) if True
Returns:: Product of theta and the effective Hamiltonian.
Return type:: theta Array

combine_Heff(env, left=True, right=True)[source]

Combine LP and RP with W to form LHeff and RHeff.

Combine LP with W0 and RP with W1 to get the effective parts of the Hamiltonian with piped legs.

Parameters:

env (MPOEnvironment) – Environment for contraction <psi|H|psi>.
left (bool) – The mixer might need only one of LHeff/RHeff after the Lanczos optimization even for combine=True. These flags allow to calculate them specifically.
right (bool) – The mixer might need only one of LHeff/RHeff after the Lanczos optimization even for combine=True. These flags allow to calculate them specifically.

combine_theta(theta)[source]

Combine the legs of theta, such that it fits to how we combined the legs of self.

Parameters:: theta (Array) – Wave function with labels 'vL', 'p0', 'p1', 'vR'
Returns:: theta – Wave function with labels 'vL', 'p0', 'p1', 'vR'
Return type:: Array

to_matrix()[source]: Contract self to a matrix.

adjoint()[source]: Return the hermitian conjugate of self.

update_LP(env, i, U=None)[source]

Equivalent to env.get_LP(i, store=True); optimized for combine.

Parameters:

env (MPOEnvironment) – The same environment as given during class initialization.
i (int) – We update the part left of site i. Can optimize if i == i0 and combine is True.
U (None | Array) – The tensor on the left-most site self acts on, with combined legs after SVD. Only used if trying to optimize.

update_RP(env, i, VH=None)[source]

Equivalent to env.get_RP(i, store=True); optimized for combine.

Parameters:

env (MPOEnvironment) – The same environment as given during class initialization.
i (int) – We update the part right of site i. Can optimize if i == i0 + 2 - length and combine is True.
U (None | Array) – The tensor on the right-most site self acts on, with combined legs after SVD. Only used if trying to optimize.