Heating Phase Transition in a Periodically-Driven Classical Spin System

Periodically-driven systems are currently experiencing an unprecedented revival of interest through theoretical and experimental work on engineering novel states of matter by dressing static systems with carefully designed periodic modulations. However, the usefulness and applicability of this so-called Floquet engineering requires the stability of the periodically driven system to detrimental heating processes. We study a periodically-driven classical spin chain and show evidence that the mechanism underlying high-frequency prethermal Floquet steady states has a classical nature, and is closely related to Nekhroshev and KAM theory. We thus demonstrate that energy absorption is exponentially suppressed up to trillions (!) of driving periods, offering a stable window for Floquet engineering. Analysing the dependence of heating on the drive frequency, we find a sharp phase transition between a stable zero-temperature and a chaotic infinite-temperature states, with time playing the role of the system size. We discuss heating in two-dimensional systems, with potential interesting implications for the currently intractable higher-dimensional quantum analogue of this problem.