Subdiffusive hydrodynamics of nearly-integrable anisotropic spin chains

TL;DR

This paper investigates spin transport in nearly-integrable anisotropic Heisenberg chains, revealing subdiffusive behavior with a dynamical exponent of 4, and shows that the diffusion constant is non-perturbative in the integrability-breaking perturbation.

Contribution

It demonstrates subdiffusive spin transport in nearly-integrable chains and adapts generalized hydrodynamics to explain this non-perturbative behavior.

Findings

Spin transport is subdiffusive with z=4 up to long times.

Transport becomes diffusive at late times with a constant independent of perturbation.

Numerical evidence supports the subdiffusive and diffusive regimes.

Abstract

We address spin transport in the easy-axis Heisenberg spin chain subject to integrability-breaking perturbations. We find that spin transport is subdiffusive with dynamical exponent $z=4$ up to a timescale that is parametrically long in the anisotropy. In the limit of infinite anisotropy, transport is subdiffusive at all times; for large finite anisotropy, one eventually recovers diffusion at late times, but with a diffusion constant independent of the strength of the integrability breaking perturbation. We provide numerical evidence for these findings, and explain them by adapting the generalized hydrodynamics framework to nearly integrable dynamics. Our results show that the diffusion constant of near-integrable interacting spin chains is generically not perturbative in the integrability breaking strength.