Relaxation dynamics of local observables in integrable systems

TL;DR

This paper demonstrates that the entire post-quench dynamics of integrable systems can be derived from a minimal set of data, revealing universal power-law relaxation behavior in the Lieb-Liniger gas.

Contribution

It introduces the generalized single-particle overlap coefficient as a key tool for computing quench dynamics in integrable models, providing a universal description of relaxation.

Findings

Power-law decay of $t^{-3}$ in density-density correlations.

Universal relaxation behavior independent of interactions.

Method applicable to a broad class of integrable systems.

Abstract

We show, using the quench action approach [Caux&Essler Phys. Rev. Lett. 110 (2013)], that the whole post-quench time evolution of an integrable system in the thermodynamic limit can be computed with a minimal set of data which are encoded in what we denote the generalized single-particle overlap coefficient $s_0^{\Psi_0}(\lambda)$. This function can be extracted from the thermodynamically leading part of the overlaps between the eigenstates of the model and the initial state. For a generic global quench the shape of $s_0^{\Psi_0}(\lambda)$ in the low momentum limit directly gives the exponent for the power law decay to the effective steady state. As an example we compute the time evolution of the static density-density correlation in the interacting Lieb-Liniger gas after a quench from a Bose-Einstein condensate. This shows an approach to equilibrium with power law $t^{-3}$ which turns out to be independent of the post-quench interaction and of the considered observable.