Integrable, Mixed, and Chaotic Dynamics in a Single All-to-All Ising Spin Model

TL;DR

This paper explores the diverse dynamical behaviors, including integrable and chaotic, of a fixed-parameter all-to-all Ising spin model, revealing symmetry-dependent chaos and noise resilience.

Contribution

It introduces a novel analysis of a fixed-parameter Ising model exhibiting mixed dynamics across symmetry sectors, mapping these to kicked tops for quantum chaos insights.

Findings

System exhibits integrable, mixed, and chaotic dynamics within a single fixed parameter set.

Symmetry sectors map to kicked tops with parameters depending on sector dimension.

System remains resilient to noise when Hamiltonian norm is close to 1.

Abstract

We demonstrate that the Ising all-to-all (ATA) model exhibits a range of dynamics, from integrable to chaotic, including mixed behaviour across symmetry blocks within a single system. While other works have explored the dynamics of all-to-all systems by varying parameters, we analyse a fixed set of parameters and examine the dynamics within different blocks. In addition to investigating the dynamical properties, we show that the system remains resilient to noise when the norm of the Hamiltonian representing the noise is close to 1. Our results are presented by mapping each symmetry sector of the system to a kicked top (KT) and observing that KT parameters for each sector depend on its dimension. This system, similar to the Bunimovich billiard for classical chaos, provides a new platform for studying dynamics determined by the symmetry sector, advancing quantum chaos research.