Confined and deconfined chaos in classical spin systems

TL;DR

This paper explores two distinct types of chaos in classical spin systems, revealing how they relate to thermalization timescales through analytical and numerical studies of specific models.

Contribution

It introduces and analyzes the concepts of confined and deconfined chaos, demonstrating their different relationships with thermalization in classical spin models.

Findings

Confined chaos occurs before thermalization, with phase space trajectories remaining constrained.

Deconfined chaos leads to simultaneous chaos and thermalization on the fastest timescale.

Analytical super-integrability is established in the deconfined chaos model.

Abstract

Weakly perturbed integrable many-body systems are typically chaotic, and thermal at late times. However, there are distinct relationships between the timescales for thermalization and chaos. The typical relationship is confined chaos: when trajectories are still confined to regions in phase space with constant conserved quantities (actions), the conjugate angle variables are already unstable. Chaotic instabilities thus far precede thermalization. In a different relationship, which we term deconfined chaos, chaotic instabilities and thermalization occur on the same timescale. We investigate these two qualitatively distinct scenarios through numerical and analytical studies of two perturbed integrable classical spin models: the Ishimori spin chain (confined chaos), and the central spin model with XX interactions (deconfined chaos). We analytically establish (super)-integrability in the latter model in a microcanonical shell. Deconfined chaos emerges through the separation of phase space into large quasi-integrable regions and a thin chaotic manifold. The latter leads to chaos and thermalization on the fastest possible timescale, which is proportional to the inverse perturbation strength. This behavior is reminiscent of the quantum SYK models and strange metals.