Power-law decay of correlations after a global quench in the massive XXZ chain

TL;DR

This paper studies how correlations in the antiferromagnetic XXZ spin chain decay over time after a sudden change in anisotropy, revealing a universal power-law decay distinct from exponential decay.

Contribution

It demonstrates that the late-time correlation decay follows a universal power-law in the XXZ chain after a quench, supported by multiple analytical and numerical methods.

Findings

Correlation decay follows a $t^{-3/2}$ power-law independent of anisotropy.

Effective free-fermion model accurately describes the late-time dynamics.

Power-law decay contrasts with previously observed exponential decay.

Abstract

We investigate the relaxation dynamics of equal-time correlations in the antiferromagnetic phase of the XXZ spin-1/2 chain following a global quantum quench of the anisotropy parameter. We focus, in particular, on the relaxation dynamics starting from an initial N\'eel state. Using state-of-the-art density-matrix renormalization group simulations, the exact solution of an effective free-fermion model, and the quench-action approach within the thermodynamic Bethe ansatz, we show that the late-time relaxation is characterized by a power-law decay $\sim t^{-3/2}$ independent of anisotropy. This is in contrast to the previously studied exponential decay of the antiferromagnetic order parameter. Remarkably, the effective model describes the numerical data extremely well even on a quantitative level if higher order corrections to the leading asymptotic behavior are taken into account.