Scaling behaviour of the relaxation in quantum chains

TL;DR

This paper analytically studies the nonequilibrium dynamics of transverse magnetization in critical Ising and XX quantum chains, revealing scaling behaviors and conserved quantities in long-time evolution.

Contribution

It provides analytical derivations of magnetization profiles and identifies conserved quantities in the long-time limit for these quantum chains.

Findings

Magnetization profiles evolve into scaling forms over time

Total residual magnetization is conserved in both Ising and XX chains after transients

Different initial states lead to similar long-time scaling behaviors

Abstract

We consider the nonequilibrium time evolution of the transverse magnetization in the critical Ising and $XX$ quantum chains. For some inhomogeneously magnetized initial states we derive analytically the transverse magnetization profiles and show that they evolve into scaling forms in the long-time limit. In particular it is seen that the Ising chain exhibits some similarities with the conserved dynamics $XX$ chain. That is, after a transient regime, the total residual magnetization in the transverse direction is also conserved in the Ising case. A class of general initial states is also considered.