No spin diffusion in the spin 1/2 XXZ chain at $T=\infty$: Numerical asymptotics

TL;DR

This paper demonstrates through numerical analysis that the spin 1/2 XXZ chain at infinite temperature exhibits no spin diffusion, with the long-time decay of correlations fitting a specific asymptotic formula.

Contribution

It provides numerical evidence that the long-time behavior of the zz correlation function does not support spin diffusion in the XXZ chain at infinite temperature.

Findings

Long-time correlation decay fits a specific asymptotic form.

Decay exponent d is significantly greater than 1/2.

Confirms absence of spin diffusion in the model.

Abstract

We analyze the recent numerical computations made by Fabricius, L{\" o}w and Stolze to show that the long time behavior of the zz correlation function of the spin 1/2 XXZ chain at $T=\infty$ is very well fit by the formula $t^{-d}[A+Be^{-\gamma (t-t_0)}\cos \Omega(t-t_0)]$ where $d$ is substantially greater than 1/2. This confirms the conclusion that there is no spin diffusion in this model.