Dynamical localization in a chain of hard core bosons under periodic driving

Abstract

We study the dynamics of a one-dimensional lattice model of hard core bosons which is initially in a superfluid phase with a current being induced by applying a twist at the boundary. Subsequently, the twist is removed and the system is subjected to periodic $\delta$-function kicks in the on-site staggered potential. We present analytical expressions for the current and work done in the limit of an infinite number of kicks. Using these, we show that the current (work done) exhibit a number of dips (peaks) as a function of the driving frequency and eventually saturates to zero (a finite value) in the limit of large frequency; these are also checked numerically. The vanishing of the current (and the saturation of the work done) in the large frequency limit can be attributed to a dynamic localization of the hard core bosons under the periodic driving. More interestingly, we show that for some specific values of the driving amplitude, the current vanishes after an infinite number of kicks for any value of the driving frequency.