Survival of current in a periodically driven hard-core bosonic system

TL;DR

This paper investigates the long-time current behavior in a periodically driven hard-core bosonic chain with double delta-function kicks, revealing the absence of dynamical localization and analyzing the system's response at various driving frequencies.

Contribution

It provides analytical and numerical insights into the current and work-done in a double kicked HCB system, highlighting differences from single kick scenarios and exploring particle spreading dynamics.

Findings

No complete current disappearance at high frequencies.

Saturated current proportional to initial twist for small initial currents.

Particles spread linearly in a light-cone region with non-zero maximum group velocity.

Abstract

We study the survival of the current induced initially by applying a twist at the boundary of a chain of hard-core bosons (HCBs), subject to a periodic double $\delta$-function kicks in the staggered on-site potential. We study the current flow and the work-done on the system at the long-time limit as a function of the driving frequency. Like a recent observation in the HCB chain with single $\delta$-function kick in the staggered on-site potential, here we also observe many dips in the current flow and concurrently many peaks in the work-done on the system at some specific values of the driving frequency. However, unlike the single kicked case, here we do not observe a complete disappearance of the current in the limit of a high driving frequency, which shows the absence of any dynamical localization in the double $\delta$-functions kicked HCB chain. Our analytical estimations of the saturated current and the saturated work-done, defined at the limit of a large time together with a high driving frequency, match very well with the exact numerics. In the case of the very small initial current, induced by a very small twist $\nu$, we observe that the saturated current is proportional to $\nu$. Finally, we study the time-evolution of the half-filled HCB chain where the particles are localized in the central part of the chain. We observe that the particles spread linearly in a light-cone like region at the rate determined by the maximum value of the group velocity. Except for a very trivial case, the maximum group velocity never vanishes, and therefore we do not observe any dynamical localization in the system.