Estimating heating times in periodically driven quantum many-body systems via avoided crossing spectroscopy

Periodic driving of a quantum (or classical) many-body system can alter the system's properties significantly and therefore has emerged as a promising way to engineer exotic quantum phases, such as topological insulators and discrete time crystals. A major limitation in such setups, is that generally interacting, driven systems will heat up over time and lose the desired properties. Understanding the relevant timescales is thus an important topic in the field and so far, there have only been a few approaches to determine heating times for a concrete system quantitatively, and in a computationally efficient way. In this paper, we propose a new approach, based on building the heating rate from microscopic processes, encoded in avoided level crossings of the Floquet propagator. We develop a method able to resolve individual crossings and show how to construct the heating rate based on these. The method is closely related to the Fermi golden rule approach for weak drives, but can go beyond it, since it captures nonperturbative effects by construction. This enables our method to be applicable in scenarios such as the heating time of discrete time crystals or frequency-dependent couplings, which are very relevant for Floquet engineering, where previously no efficient methods for estimating heating times were available.