From stable periodic orbits to many-body chaos: doubly tunable prethermalization via engineering of an emergent band structure

Abstract

We uncover a family of many-body periodic orbits in a periodically driven (Floquet) spin system away from the high-frequency limit. While linear stability analysis predicts that perturbed many-body trajectories remain close to stable periodic orbits, thermodynamic principles dictate that Floquet heating will ultimately set in. Our work aims to resolve the tension between these two expectations. In particular, we show that perturbations away from the stable periodic orbits feature a description akin to a quasiparticle band structure. A long-lived prethermal regime appears when modes around the gapless point are slowly populated. The dispersion determines the prethermal lifetime, and we show how band engineering leads to a "doubly tunable" parametric dependence of the prethermal lifetime $R^{-W}$, with $R$ the width in momentum space of the quasiparticle distribution and $W$ the exponent of the dispersion around the gapless point. Our results not only establish a powerful route toward stabilizing non-equilibrium phases of matter in driven many-body systems but also establish a conceptual bridge between periodic orbits in 'low-dimensional' nonlinear systems and many-body chaos.