Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions

TL;DR

This paper explores how chaos influences long-time dynamics and diffusion behaviors across phase transitions in a classical spin model, revealing distinct chaotic and diffusive regimes in different phases.

Contribution

It demonstrates the connection between chaos and collective mode dynamics across phase transitions, with new insights into classical and semiclassical quantum systems.

Findings

Chaos exhibits crossovers across phase transitions.

Normal diffusion occurs in high-temperature phases.

Anomalous diffusion occurs in low-temperature phases.

Abstract

Chaos is an important characterization of classical dynamical systems. How is chaos linked to the long-time dynamics of collective modes across phases and phase transitions? We address this by studying chaos across Ising and Kosterlitz-Thouless transitions in classical XXZ model. We show that spatio-temporal chaotic properties have crossovers across the transitions and distinct temperature dependence in the high and low-temperature phases which show normal and anomalous diffusions, respectively. Our results also provide new insights into the dynamics of interacting quantum systems in the semiclassical limit.