Quench dynamics and relaxation in isolated integrable quantum spin chains

TL;DR

This paper reviews the relaxation dynamics in isolated integrable quantum spin chains after a quench, highlighting the role of generalized Gibbs ensembles and recent advances in understanding key models like the transverse field Ising and Heisenberg chains.

Contribution

It provides a comprehensive overview of quench dynamics in integrable quantum spin chains, including pedagogical explanations and recent progress in key models.

Findings

Relaxation to steady states described by generalized Gibbs ensembles.

Time evolution of local observables analyzed using free fermion models.

Recent progress in understanding dynamics of the transverse field Ising and Heisenberg chains.

Abstract

We review the dynamics after quantum quenches in integrable quantum spin chains. We give a pedagogical introduction to relaxation in isolated quantum systems, and discuss the description of the steady state by (gen- eralized) Gibbs ensembles. When then turn to general features in the time evolution of local observables after the quench, using a simple model of free fermions as an example. In the second part we present an overview of recent progress in describing quench dynamics in two key paradigms for quantum integrable models, the transverse field Ising chain and the anisotropic spin-1/2 Heisenberg chain.