Broken Ergodicity in classically chaotic spin systems

TL;DR

This paper investigates how the range of interactions in a chaotic spin chain affects ergodicity, revealing a persistent non-ergodic phase in models with all-to-all coupling below a certain energy threshold.

Contribution

It analytically identifies the energy threshold for ergodicity breaking in a classically chaotic XY spin model with asymmetric interactions.

Findings

Non-ergodicity persists with all-to-all interactions below a specific energy threshold.

Ergodicity and chaoticity depend strongly on interaction range.

Analytical expression for the energy threshold is provided.

Abstract

A one dimensional classically chaotic spin chain with asymmetric coupling and two different inter-spin interactions, nearest neighbors and all-to-all, has been considered. Depending on the interaction range, dynamical properties, as ergodicity and chaoticity are strongly different. Indeed, even in presence of chaoticity, the model displays a lack of ergodicity only in presence of all to all interaction and below an energy threshold, that persists in the thermodynamical limit. Energy threshold can be found analytically and results can be generalized for a generic XY model with asymmetric coupling.