In this work we study the entanglement entropy of a uniform quantum Ising chain in transverse field undergoing a periodic driving of period τ. By means of Floquet theory we show that, for any subchain, the entanglement entropy tends asymptotically to a value τ-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.

Entanglement entropy in a periodically driven Ising chain / Russomanno, Angelo; Santoro, Giuseppe E.; Fazio, Rosario. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 2016:Jul(2016), pp. 1-27. [10.1088/1742-5468/2016/07/073101]

Entanglement entropy in a periodically driven Ising chain

Russomanno, Angelo;Santoro, Giuseppe E.;
2016

Abstract

In this work we study the entanglement entropy of a uniform quantum Ising chain in transverse field undergoing a periodic driving of period τ. By means of Floquet theory we show that, for any subchain, the entanglement entropy tends asymptotically to a value τ-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.
2016
Jul
1
27
073101
https://iopscience.iop.org/article/10.1088/1742-5468/2016/07/073101/meta
https://arxiv.org/abs/1603.03663
Russomanno, Angelo; Santoro, Giuseppe E.; Fazio, Rosario
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/87945
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