Spin diffusion in perturbed isotropic Heisenberg spin chain

TL;DR

This paper investigates spin diffusion in the isotropic Heisenberg chain, revealing nonmonotonic diffusion behavior and superdiffusion at specific anisotropy, with implications for understanding transport in quantum many-body systems.

Contribution

It demonstrates that the isotropic Heisenberg model exhibits stable superdiffusive spin transport at finite magnetization and anisotropy, even with SU(2) invariant perturbations.

Findings

Nonmonotonic dependence of diffusion constant on anisotropy.

Superdiffusion at anisotropy Δ=1 remains stable under perturbations.

Behavior consistent with recent cold atom experiments.

Abstract

The isotropic Heisenberg chain represents a particular case of an integrable many-body system exhibiting superdiffusive spin transport at finite temperatures. Here, we show that this model has distinct properties also at finite magnetization $m\ne0$, even upon introducing the SU(2) invariant perturbations. Specifically, we observe nonmonotonic dependence of the diffusion constant ${\cal D}_0(\Delta)$ on the spin anisotropy $\Delta$, with a pronounced maximum at $\Delta =1$. The latter dependence remains true also in the zero magnetization sector, with superdiffusion at $\Delta=1$ that is remarkably stable against isotropic perturbation (at least in finite-size systems), consistent with recent experiments with cold atoms.