Entanglement entropy in a periodically driven quantum Ising chain

TL;DR

This paper investigates how entanglement entropy evolves in a periodically driven quantum Ising chain, revealing synchronization with the drive, quasi-revivals, and volume law scaling without heating to infinite temperature.

Contribution

It provides a detailed numerical analysis of entanglement dynamics under periodic driving, highlighting synchronization phenomena and the persistence of integrability.

Findings

Entanglement entropy synchronizes with the periodic drive.

Quasi-revivals appear and fade out in the thermodynamic limit.

Entanglement entropy follows a volume law scaling in the long-time average.

Abstract

We numerically study the dynamics of entanglement entropy, induced by an oscillating time periodic driving of the transverse field, h(t), of a one-dimensional quantum Ising chain. We consider several realizations of h(t), and we find a number of results in analogy with entanglement entropy dynamics induced by a sudden quantum quench. After short-time relaxation, the dynamics of entanglement entropy synchronises with h(t), displaying an oscillatory behaviour at the frequency of the driving. Synchronisation in the dynamics of entanglement entropy, is spoiled by the appearance of quasi-revivals which fade out in the thermodynamic limit, and which we interpret using a quasi-particle picture adapted to periodic drivings. Taking the time-average of the entanglement entropy in the synchronised regime, we find that it obeys a volume law scaling with the subsystem's size. Such result is reminiscent of a thermal state or of a Generalised Gibbs ensemble of a quenched Ising chain, although the system does not heat up towards infinite temperature as a consequence of the integrability of the model.