How many-body chaos emerges in the presence of quasiparticles

TL;DR

This paper develops a theory describing how many-body chaos emerges from the scattering of quasiparticles, using a classical Heisenberg chain model to illustrate the cascade of lightcones leading to chaos.

Contribution

It introduces a framework linking quasiparticle scattering to the onset of many-body chaos through a cascade of lightcones and chaos diagnostics.

Findings

Short-time integrable regime observed

Intermediate scarred regime identified

Transition to chaos via scattering avalanche

Abstract

Many-body chaos is a default property of many-body systems; at the same time, near-integrable behaviour due to weakly interacting quasiparticles is ubiquitous throughout condensed matter at low temperature. There must therefore be a, possibly generic, crossover between these very different regimes. Here, we develop a theory encapsulating the notion of a cascade of lightcones seeded by sequences of scattering of weakly interacting harmonic modes as witnessed by a suitably defined chaos diagnostic (classical decorrelator) that measures the spatiotemporal profile of many-body chaos. Our numerics deals with the concrete case of a classical Heisenberg chain, for either sign of the interaction, at low temperatures where the short-time dynamics are well captured in terms of non-interacting spin waves. To model low-temperature dynamics, we use ensembles of initial states with randomly embedded point defects in an otherwise ordered background, which provides a controlled setting for studying the scattering events. The decorrelator exhibits a short-time integrable regime followed by an intermediate `scarred' regime of the cascade of lightcones in progress; these then overlap, leading to an avalanche of scattering events which finally yields the standard long-time signature of many-body chaos.