Entanglement generation and dynamical transition for driven quantum integrable systems.

In this talk, we shall discuss the generation of entanglement entropy S of a closed quantum system driven periodically with frequency w and for n drive cycles. We show that such a drive may be used to generate states for which th scaling of S lies between an area and a volume law. We provide a qualitative criterion for the change in nature of S which constitutes a generalization of Hastings\' theorem to driven integrable systems. We also find that S and any correlation function of such a driven system decay to their steady state values as (w/n)^[(d+2)/2] for fast and (w/n)^[d/2] for slow drives; these two dynamical phases are separated by a transition associated with the change in topology of the spectrum of the system\'s Floquet Hamiltonian. We show that these dynamical phases show re-entrant behavior as a function of w for d = 1 (and a class of d = 2) models, provide a detailed phase diagram of the system, and discuss experiments which can test our theory.