Anomalous Floquet Heating from Sparse Long-Range Interactions

Abstract

Regular lattices of interacting particles under a periodic drive typically heat with rate $\gamma \sim e^{-\mathcal{O}(\omega)}$ which is exponentially suppressed in drive frequency $\omega$. Here, we show that sparse infinite-range interactions, which have recently become accessible in quantum simulators, can lead to anomalous heating with rate $\gamma \sim e^{-\mathcal{O}(\sqrt{\omega})}$. This anomaly originates from the broad distribution of coordination numbers across the network: as the driving frequency increases, heating becomes dominated by sites with larger coordination numbers, making the characteristic local energy scale relevant for heating grow with frequency. For small-world networks, we develop an analytic theory that thoroughly matches our large scale numerics. Finally, we discuss how network topology can serve as a control knob for engineering non-equilibrium phases of matter. Our results uncover a new mechanism for Floquet heating and suggest new routes toward stabilizing nonequilibrium phases in driven systems with programmable interaction networks.