From single-particle to many-body chaos in Yukawa--SYK: theory and a cavity-QED proposal

TL;DR

This paper explores the Yukawa--SYK model as a bridge between single-particle and many-body quantum chaos, providing a comprehensive analysis and proposing an experimental cavity-QED implementation.

Contribution

It introduces the YSYK model as a tunable framework connecting different chaos regimes and offers a detailed finite-size characterization and experimental proposal.

Findings

YSYK interpolates between SYK2 and SYK4 limits

Intermediate regimes show partial ergodicity breaking

Feasible cavity-QED implementation proposed

Abstract

Understanding how quantum systems transition from integrable to fully chaotic behavior remains a central open problem in physics. The Sachdev--Ye--Kitaev (SYK) model provides a paradigmatic framework for studying many-body chaos and holography, yet it captures only the strongly correlated limit, leaving intermediate regimes unexplored. Here, we investigate the Yukawa--SYK (YSYK) model, where bosonic fields mediate random fermionic interactions, and demonstrate that it naturally bridges single-particle and many-body chaos. Using spectral and dynamical chaos markers, we perform a comprehensive finite-size characterization of the YSYK model. We show that the interaction strength acts as a tunable control parameter interpolating between the SYK$_2$ and SYK$_4$ limits, and introduce a framework enabling direct and quantitative comparison with these benchmark models. In the intermediate regimes, we uncover distinct dynamical regimes marked by partial ergodicity breaking, prethermalization plateaus, and incomplete scrambling. Finally, we propose a feasible optical-cavity implementation of the YSYK model using ultra-cold atoms. Our results establish the YSYK model as a unifying platform connecting single-particle and many-body chaos, paving the way for experimental observation of these phenomena.