Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench

TL;DR

This paper investigates how antiferromagnetic order in spin-1/2 chains relaxes after a quantum quench, revealing exponential decay and a unique relaxation time behavior at the critical point.

Contribution

It provides a detailed analysis of the relaxation dynamics of antiferromagnetic order in anisotropic Heisenberg chains post-quench, highlighting the behavior at the critical point.

Findings

Antiferromagnetic order decays exponentially over time.

Relaxation dynamics can be oscillatory or non-oscillatory depending on anisotropy.

Relaxation time peaks at the critical point, contrary to typical critical slowing down.

Abstract

We study the unitary time evolution of antiferromagnetic order in anisotropic Heisenberg chains that are initially prepared in a pure quantum state far from equilibrium. Our analysis indicates that the antiferromagnetic order imprinted in the initial state vanishes exponentially. Depending on the anisotropy parameter, oscillatory or non-oscillatory relaxation dynamics is observed. Furthermore, the corresponding relaxation time exhibits a at the critical point, in contrast to the usual notion of critical slowing down, from which a maximum is expected.