Mean-field dynamics of an infinite-range interacting quantum system: Chaos, dynamical phase transition, and localization

We investigate the dynamical properties of the XY spin -1/2 chain with infinite -range transverse interactions and find a dynamical phase transition with a chaotic dynamical phase. In the latter, we find nonvanishing finitetime Lyapunov exponents and intermittent behavior signaled by fast and slow entropy growth periods. Further, we study the XY chain with a local self -consistent transverse field and observe a localization phase transition. We show that localization stabilizes the chaotic dynamical phase.