Relaxation dynamics in the gapped XXZ spin-1/2 chain

TL;DR

This paper investigates the non-thermalizing relaxation dynamics of a domain wall state in the gapped XXZ spin-1/2 chain, providing exact solutions and proving the system's failure to thermalize.

Contribution

It offers an exact analytical approach to study the dynamics of the gapped XXZ chain and proves non-thermalization in the gapped regime.

Findings

Exact wavefunctions describe long-time dynamics accurately.

The gapped regime ($ >1$) does not thermalize.

Rigorous proof of non-thermalization in the gapped phase.

Abstract

We study the dynamics of a quench-prepared domain wall state released into a system whose unitary time evolution is dictated by the Hamiltonian of the Heisenberg spin-1/2 gapped antiferromagnetic chain. Using exact wavefunctions and their overlaps with the domain wall state allows us to describe the release dynamics to high accuracy, up to the long-time limit, for finite as well as infinite systems. The results for the infinite system allow us to rigorously prove that the system in the gapped regime ($\Delta >1$) cannot thermalize in the strict sense.