Anomalous Dynamics and Equilibration in the Classical Heisenberg Chain

TL;DR

This paper investigates spin dynamics in the classical Heisenberg chain, revealing distinct diffusive behaviors in ferromagnetic and antiferromagnetic regimes, with implications for understanding equilibration in low-dimensional systems.

Contribution

It provides the first detailed numerical comparison of spin transport in ferromagnetic and antiferromagnetic Heisenberg chains across various temperatures.

Findings

Antiferromagnet exhibits largely diffusive spin dynamics.

Ferromagnet shows evidence of super-diffusion or slow crossover to diffusion.

Differences in dynamics persist even at high temperatures.

Abstract

The search for departures from standard hydrodynamics in many-body systems has yielded a number of promising leads, especially in low dimension. Here we study one of the simplest classical interacting lattice models, the nearest-neighbour Heisenberg chain, with temperature as tuning parameter. Our numerics expose strikingly different spin dynamics between the antiferromagnet, where it is largely diffusive, and the ferromagnet, where we observe strong evidence either of spin super-diffusion or an extremely slow crossover to diffusion. This difference also governs the equilibration after a quench, and, remarkably, is apparent even at very high temperatures.