quimb.tensor.tn1d.tebd¶

Tools for performing TEBD like algorithms in 1D.

Attributes¶

NNI

Classes¶

`LocalHam1D`	An simple interacting hamiltonian object used, for instance, in TEBD.
`TEBD`	Class implementing Time Evolving Block Decimation (TEBD) [1].

Functions¶

OTOC_local(psi0, H, H_back, ts, i, A[, j, B, ...])

The out-of-time-ordered correlator (OTOC) generating by two local

Module Contents¶

class quimb.tensor.tn1d.tebd.LocalHam1D(L, H2, H1=None, cyclic=False)[source]¶

Bases: quimb.tensor.tnag.tebd.LocalHamGen

An simple interacting hamiltonian object used, for instance, in TEBD. Once instantiated, the LocalHam1D hamiltonian stores a single term per pair of sites, cached versions of which can be retrieved like H.get_gate_expm((i, i + 1), -1j * 0.5) etc.

Parameters:

L (int) – The size of the hamiltonian.
H2 (array_like or dict[tuple[int], array_like]) – The sum of interaction terms. If a dict is given, the keys should be nearest neighbours like (10, 11), apart from any default term which should have the key None, and the values should be the sum of interaction terms for that interaction.
H1 (array_like or dict[int, array_like], optional) – The sum of single site terms. If a dict is given, the keys should be integer sites, apart from any default term which should have the key None, and the values should be the sum of single site terms for that site.
cyclic (bool, optional) – Whether the hamiltonian has periodic boundary conditions or not.

terms¶

The terms in the hamiltonian, combined from the inputs such that there is a single term per pair.

Type:: dict[tuple[int], array]

Examples

A simple, translationally invariant, interaction-only LocalHam1D:

>>> XX = pauli('X') & pauli('X')
>>> YY = pauli('Y') & pauli('Y')
>>> ham = LocalHam1D(L=100, H2=XX + YY)

The same, but with a translationally invariant field as well:

>>> Z = pauli('Z')
>>> ham = LocalHam1D(L=100, H2=XX + YY, H1=Z)

Specifying a default interaction and field, with custom values set for some sites:

>>> H2 = {None: XX + YY, (49, 50): (XX + YY) / 2}
>>> H1 = {None: Z, 49: 2 * Z, 50: 2 * Z}
>>> ham = LocalHam1D(L=100, H2=H2, H1=H1)

Specifying the hamiltonian entirely through site specific interactions and fields:

>>> H2 = {(i, i + 1): XX + YY for i in range(99)}
>>> H1 = {i: Z for i in range(100)}
>>> ham = LocalHam1D(L=100, H2=H2, H1=H1)