From single-particle to many-body chaos in the Yukawa-Sachdev-Ye-Kitaev model: Theory and a cavity-QED proposal

Abstract

Understanding how quantum systems evolve from integrable to fully chaotic behavior remains a central open problem in physics. In this work, we show that the Yukawa-Sachdev-Ye-Kitaev (YSYK) model is a particularly rich testbed to address this question. This model extends the paradigmatic SYK model of many-body chaos and holography by introducing boson-mediated random all-to-all fermionic interactions. Using spectral and dynamical chaos markers, we perform a comprehensive numerical characterization tailored to the mesoscopic regime relevant for quantum simulation. We show that, at finite size, the YSYK model interpolates between single-particle and many-body chaos, with the interaction strength acting as a tunable control parameter interpolating between SYK2 and SYK4 behavior. We introduce a framework enabling direct and quantitative comparison with these benchmark models, and we uncover prethermalization plateaus as well as delayed and incomplete scrambling appearing in an intermediate regime that weakly breaks integrability. We further propose a feasible optical-cavity realization of the YSYK model using ultracold atoms, opening the door to studies beyond the capacities of numerical investigations. Our results establish the YSYK model as a benchmark platform connecting single-particle and many-body chaos, and they provide a quantitative reference point for future quantum simulations.