Anomalous dynamics and equilibration in the classical Heisenberg chain

Adam J Mcroberts,Thomas Bilitewski,Masudul Haque,Roderich Moessner

doi:10.1103/physrevb.105.l100403

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.

Highlights

The search for departures from standard hydrodynamics in many-body systems has yielded a number of promising leads, especially in low dimensions
Hydrodynamics has long been a cornerstone of our understanding of many-body systems, and has recently become the focus of renewed inquiry
Based on the lack of integrability, it has been argued that ordinary diffusion holds for both spin and energy [55–61]

Summary

Introduction

Hydrodynamics has long been a cornerstone of our understanding of many-body systems, and has recently become the focus of renewed inquiry. We find a qualitative difference between ferromagnetic and antiferromagnetic models at finite temperatures This manifests as a temperature-dependent finite-time dynamical exponent in the spin correlations of the ferromagnetic chain, which departs from the diffusive exponent α = 1/2, whereas the antiferromagnetic chain displays behavior compatible with spin diffusion at all temperatures studied. The spacetime profiles of correlation functions closely follow the KPZ scaling form This establishes intermediate-time KPZ scaling at low temperatures in the FM Heisenberg model, even if followed by a crossover to normal diffusion at very long times. Equilibration is shown to proceed via a power-law approach

Published by the American Physical Society

Discussion and conclusions