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-ETH for slow driving/weak disorder) and many-body localized (Floquet-MBL 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. 
Jorge Rehn and Achilleas Lazarides and Frank Pollmann and Roderich   Moessner
cond-mat.stat-mech cond-mat.dis-nn