Semiclassical Prediction of Large Spectral Fluctuations in Interacting Kicked Spin Chains

TL;DR

This paper develops a semiclassical approach to analyze spectral fluctuations in many-body quantum systems, specifically kicked interacting spin chains, revealing complex behavior that blurs the line between integrability and chaos.

Contribution

It introduces a duality-based semiclassical method for many-body systems and uncovers how interactions create collective dynamics affecting spectral fluctuations.

Findings

Spectral fluctuations are significantly enhanced due to collective periodic orbits.

The system exhibits behavior intermediate between integrable and chaotic regimes.

A new duality approach aids in semiclassical analysis of many-body quantum chaos.

Abstract

While plenty of results have been obtained for single-particle quantum systems with chaotic dynamics through a semiclassical theory, much less is known about quantum chaos in the many-body setting. We contribute to recent efforts to make a semiclassical analysis of many-body systems feasible. This is nontrivial due to both the enormous density of states and the exponential proliferation of periodic orbits with the number of particles. As a model system we study kicked interacting spin chains employing semiclassical methods supplemented by a newly developed duality approach. We show that for this model the line between integrability and chaos becomes blurred. Due to the interaction structure the system features (non-isolated) manifolds of periodic orbits possessing highly correlated, collective dynamics. As with the invariant tori in integrable systems, their presence lead to significantly enhanced spectral fluctuations, which by order of magnitude lie in-between integrable and chaotic cases.