Multiple relaxation times in perturbed XXZ chain

TL;DR

This paper investigates how correlation functions in a perturbed XXZ chain relax at different rates, revealing multiple relaxation times linked to conserved quantities and non-exponential decay behaviors.

Contribution

It demonstrates the existence of multiple relaxation times in the perturbed XXZ chain, depending on magnetization and conserved quantities, advancing understanding of non-equilibrium dynamics in integrable systems.

Findings

Correlation functions exhibit multiple relaxation rates at finite magnetization.

Decay of non-commuting quantities is non-exponential with a linear dependence on perturbation strength.

Different conserved quantities are associated with distinct relaxation times.

Abstract

We numerically study the relaxation of correlation functions in weakly perturbed integrable XXZ chain. The decay of the spin-current and the energy-current correlations at zero magnetization are well described by single, but quite distinct, relaxation rates governed by the square of the perturbation strength $g$. However, at finite magnetization a single correlation function reveals multiple relaxation rates. The result can be understood in terms of multi-scale relaxation scenario, where various relaxation times are linked with various quantities which are conserved in the reference integrable system. On the other hand, the correlations of non-commuting quantities, being conserved at particular anisotropies $\Delta$, decay non-exponentially with characteristic time scale linear in $g$.