How periodic driving heats a disordered quantum spin chain

We study the energy absorption in real time of a disordered quantum spin chain subjected to coherent monochromatic periodic driving. We determine characteristic fingerprints of the well-known ergodic (Floquet-Eigenstate thermalization hypothesis for slow driving/weak disorder) and many-body localized (Floquet-many-body localization for fast driving/strong disorder) phases. In addition, we identify an intermediate regime, where the energy density of the system-unlike the entanglement entropy a local and bounded observable-grows logarithmically slowly over a very large time window.