Fate of diffusion under integrability breaking of classical integrable magnets

TL;DR

This study investigates how integrability-breaking perturbations affect spin diffusion in a classical Landau-Lifshitz magnet, revealing a sharp transition in diffusion behavior and a change in statistical transfer properties.

Contribution

It provides large-scale numerical evidence of a sharp diffusion transition and statistical crossover in classical integrable magnets under perturbations.

Findings

Sharp change in spin diffusion constant with perturbation strength

Crossover from non-Gaussian to Gaussian magnetization transfer statistics

Hints at non-trivial diffusion mechanisms in integrable systems

Abstract

Diffusive transport is a ubiquitous phenomenon, yet the microscopic origin of diffusion in interacting physical systems remains a challenging question, irrespective of whether quantum effects are dominant or not. In this work, we study infinite temperature spin diffusion in a classical integrable, space-time discrete version of anisotropic Landau-Lifshitz magnet in the easy-axis regime, subjected to integrability-breaking perturbations. Our numerical results based on large-scale simulations reveal i) a sharp change in the spin diffusion constant as a function of perturbation strength in the thermodynamic limit and ii) a crossover from non-Gaussian to Gaussian statistics of magnetization transfer reflected in higher order cumulants under integrability breaking. Both our observations hint to the presence of non-trivial diffusion mechanism inherent to integrable systems.