Quasi-conserved quantities in the perturbed XXX spin chain

TL;DR

This paper investigates how certain conserved quantities in the isotropic Heisenberg spin chain are approximately preserved under small local perturbations, explaining the emergence of prethermalization.

Contribution

It introduces a method to modify local integrals of motion to create quasi-conserved charges in the perturbed model, highlighting limitations for higher-order integrals.

Findings

Only the first few integrals of motion become quasi-conserved under perturbation.

Higher-order integrals do not survive as quasi-conserved quantities.

Quasi-conserved charges are linked to prethermalization phenomena.

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 only the first few integrals of motion can be promoted to the quasi-conserved charges, whereas higher-order integrals of motion do not survive.