Entanglement entropy in a periodically driven Ising chain

TL;DR

This paper investigates the entanglement entropy dynamics in a periodically driven quantum Ising chain, revealing asymptotic periodic behavior, a volume law, and connections to non-equilibrium phase transitions via Floquet theory.

Contribution

It provides a semi-analytical formula for the asymptotic entanglement entropy in a driven Ising chain, linking it to the GGE and non-equilibrium phase transitions.

Findings

Entanglement entropy tends to a τ-periodic value over time.

The asymptotic entropy obeys a volume law and is below thermal entropy.

Features in the entropy correspond to non-equilibrium quantum phase transitions.

Abstract

In this work we study the entanglement entropy of a uniform quantum Ising chain in transverse field undergoing a periodic driving of period $\tau$ . By means of Floquet theory we show that, for any subchain, the entanglement entropy tends asymptotically to a value $\tau$ - periodic in time. We provide a semi-analytical formula for the leading term of this asymptotic regime: It is constant in time and obeys a volume law. The entropy in the asymptotic regime is always smaller than the thermal one: because of integrability the system locally relaxes to a Generalized Gibbs Ensemble (GGE) density matrix. The leading term of the asymptotic entanglement entropy is completely determined by this GGE density matrix. Remarkably, the asymptotic entropy shows marked features in correspondence to some non-equilibrium quantum phase transitions undergone by a Floquet state analog of the ground state.