Approximate conservation laws in perturbed integrable lattice models

TL;DR

The paper introduces a numerical method to identify approximately conserved quantities in perturbed integrable lattice models, revealing how perturbations expand the support of these quantities and confirming the validity of perturbation theory.

Contribution

A new numerical algorithm for detecting approximate conservation laws in non-integrable models, with application to the perturbed XXZ model.

Findings

Perturbations expand the support of conserved quantities quadratically with perturbation strength.

Correlation functions of conserved quantities support the perturbation theory.

The method confirms the role of approximate conserved quantities in long-time dynamics.

Abstract

We develop a numerical algorithm for identifying approximately conserved quantities in models perturbed away from integrability. In the long-time regime, these quantities fully determine correlation functions of local observables. Applying the algorithm to the perturbed XXZ model we find that the main effect of perturbation consists in expanding the support of conserved quantities. This expansion follows quadratic dependence on the strength of perturbation. The latter result together with correlation functions of conserved quantities obtained from the memory function analysis confirm feasibility of the perturbation theory.