Coexistence of different scaling laws for the entanglement entropy in a periodically driven system

TL;DR

This paper investigates the entanglement entropy dynamics in a periodically driven 1D quantum Ising model, revealing coexistence of different scaling laws and persistent critical-like behavior under sinusoidal drive.

Contribution

It demonstrates the coexistence of area and volume laws for entanglement entropy under periodic driving and explains this phenomenon via Floquet quasi-particle propagation.

Findings

Area and volume law coexist for non-critical initial states.

Critical-like entanglement scaling persists for large subsystems.

Finite size scaling observed even under periodic drive.

Abstract

The out-of-equilibrium dynamics of many body systems has recently received a burst of interest, also due to experimental implementations. The dynamics of both observables, such as magnetization and susceptibilities, and quantum information related quantities, such as concurrence and entanglement entropy, have been investigated under different protocols bringing the system out of equilibrium. In this paper we focus on the entanglement entropy dynamics under a sinusoidal drive of the transverse magnetic field in the 1D quantum Ising model. We find that the area and the volume law of the entanglement entropy coexist under periodic drive for an initial non-critical ground state. Furthermore, starting from a critical ground state, the entanglement entropy exhibits finite size scaling even under such a periodic drive. This critical-like behaviour of the out-of-equilibrium driven state can persist for arbitrarily long time, provided that the entanglement entropy is evaluated on increasingly subsystem sizes, whereas for smaller sizes a volume law holds. Finally, we give an interpretation of the simultaneous occurrence of critical and non-critical behaviour in terms of the propagation of Floquet quasi-particles.