Anomalous transport in non-integrable classical field theories

TL;DR

This paper investigates anomalous spin transport in non-integrable classical field theories, revealing temperature-dependent regimes of superdiffusion, ballistic, and diffusive behaviors, with evidence of soliton-like structures at low temperatures.

Contribution

It demonstrates that finite temperature can restore anomalous transport in non-integrable continuum models and characterizes the crossover between different transport regimes.

Findings

Spin superdiffusion with KPZ scaling at low temperature for n=1

Crossover from superdiffusive to diffusive transport with increasing temperature

Presence of long-lived soliton-like trajectories at low temperature

Abstract

Anomalous KPZ spin transport is well established in integrable non-Abelian lattice models but has not been investigated in continuum field theories as discretization in numerics generally break the continuum theory's integrability. We show that finite temperature acts as a regulator that can restore anomalous transport over a broad time window. In a family of spin field theories labeled by integer $n$, the $n = 1$ case is the Landau-Lifshitz model, whose numerical data shows spin superdiffusion with Kardar-Parisi-Zhang (KPZ) scaling and, at lower temperature ballistic energy transport, whereas both observables are diffusive at high temperature. The non-integrable $n = 2$ case shows the same crossover. While Lyapunov analysis confirms the model's non-integrability, the structure of spin-density space-time profiles suggests that long-lived soliton-like trajectories exist at low temperature.