Long-range correlation and the spin conductivity in the XXZ chain from ballistic macroscopic fluctuation theory

TL;DR

This paper uses ballistic macroscopic fluctuation theory to analyze spin conductivity and long-range correlations in the critical XXZ chain, revealing temperature-dependent transport behaviors and dynamic scaling insights.

Contribution

It introduces a novel analysis linking long-range correlations to superdiffusive spin transport in the XXZ chain at criticality.

Findings

Spin conductivity is proportional to 1/T at high temperatures.

Long-range spin correlations scale as 1/N, influencing superdiffusive transport.

High temperature proportionality constant diverges with infinite quasiparticle magnetization.

Abstract

Based on the ballistic macroscopic fluctuation theory, the integration of the spin correlation function (spin conductivity) is analyzed for the spin-1/2 XXZ chain in the critical regime. In the time when the magnetization of an infinite spin chain fluctuates from an initial state with a wavelength as long as the infinite length $N$, the equal-time two-point spin correlation function is scaled up to $O(1/N)$. In the state where the ballistic spin transport decays at high temperature $T$, the diffusive transport remains on a large scale. We show that the spin conductivity is proportional to $1/T$ in the limit $T\to\infty$ and its high temperature proportionality constant diverges in the case where one-quasiparticle magnetization is infinitely large. This analysis informs that the superdiffusive spin transport is driven by the $1/N$-scaled long-range spin correlation and sheds a light on the dynamic scaling in spin transport at the isotropic point.