Quasi-conserved charges in the perturbed spin-1/2 XXX model

TL;DR

This paper constructs explicit quasi-conserved charges in a weakly perturbed spin-1/2 Heisenberg chain, providing insights into prethermalization phenomena in nearly integrable quantum systems.

Contribution

It introduces a method to modify local integrals of motion to obtain quasi-conserved quantities in a perturbed Heisenberg model, highlighting their role in prethermalization.

Findings

Existence of quasi-conserved charges for local perturbations

Explicit construction of the first few quasi-conserved charges

Implication for understanding prethermalization phases

Abstract

We consider the isotropic spin-$1/2$ Heisenberg spin chain weakly perturbed by a local translationally- and $SU(2)$-invariant perturbation. Starting from the local integrals of motion of the unperturbed model, we modify them in order to obtain quasi-conserved integrals of motion (charges) for the perturbed model. Such quasi-conserved quantities are believed to be responsible for the existence of the prethermalization phase at intermediate timescales. We find that for a sufficiently local perturbation the quasi-conserved quantities indeed exist, and we construct an explicit form for the first few of them.