Hydrodynamic relaxation of spin helices

TL;DR

This paper develops a hydrodynamic theory combining generalized hydrodynamics and diffusive corrections to explain the relaxation dynamics of spin helices in quantum XXZ spin chains, aligning with recent cold atom experiments.

Contribution

It introduces a novel theoretical framework that accurately models spin helix relaxation, including anomalous diffusion and anisotropy effects, beyond linear response.

Findings

Reproduces experimental relaxation dynamics of spin helices.

Explains anomalous diffusion regimes observed experimentally.

Identifies asymmetry in relaxation behavior between positive and negative anisotropy.

Abstract

Motivated by recent cold atom experiments, we study the relaxation of spin helices in quantum XXZ spin chains. The experimentally observed relaxation of spin helices follows scaling laws that are qualitatively different from linear-response transport. We construct a theory of the relaxation of helices, combining generalized hydrodynamics (GHD) with diffusive corrections and the local density approximation. Although helices are far from local equilibrium (so GHD need not apply a priori), our theory reproduces the experimentally observed relaxational dynamics of helices. In particular, our theory explains the existence of temporal regimes with apparent anomalous diffusion, as well as the asymmetry between positive and negative anisotropy regimes.