Fate of dynamical many-body localization in the presence of disorder

Dynamical localization is one of the most startling manifestations of quantum interference, where the evolution of a simple system is frozen out under a suitably tuned coherent periodic drive. Here we show that, although any randomness in the interactions of a many-body system kills dynamical localization eventually, spectacular remnants survive even when the disorder is strong. We consider a disordered quantum Ising chain where the transverse magnetization relaxes exponentially with time with a decay time-scale tau due to random longitudinal interactions between the spins. We show that, under external periodic drive, this relaxation slows down (tau shoots up) by orders of magnitude as the ratio of the drive frequency omega and amplitude h(0) tends to certain specific values (the freezing condition). If omega is increased while maintaining the ratio h(0)/omega at a fixed freezing value, then tau diverges exponentially with omega. The results can be easily extended for a larger family of disordered fermionic and bosonic systems.