Entanglement revivals as a probe of scrambling in finite quantum systems. (25th August 2020)

• Record Type: Journal Article
• Authors: Modak, Ranjan; Alba, Vincenzo; Calabrese, Pasquale
• Is Part Of: Journal of statistical mechanics. (2020:Aug.)
• Publication Date: 2020-08-25
• Subjects: breaking integrability -- entanglement in extended quantum systems -- quantum quenches -- generalized gibbs ensemble; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/aba9d9
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: The entanglement evolution after a quantum quench became one of the tools to distinguish integrable versus chaotic (non-integrable) quantum many-body dynamics. Following this line of thoughts, here we propose that the revivals in the entanglement entropy provide a finite-size diagnostic benchmark for the purpose. Indeed, integrable models display periodic revivals manifested in a dip in the block entanglement entropy in a finite system. On the other hand, in chaotic systems, initial correlations get dispersed in the global degrees of freedom (information scrambling) and such a dip is suppressed. We show that while for integrable systems the height of the dip of the entanglement of an interval of fixed length decays as a power law with the total system size, upon breaking integrability a much faster decay is observed, signalling strong scrambling. Our results are checked by exact numerical techniques in free-fermion and free-boson theories, and by time-dependent density matrix renormalisation group in interacting integrable and chaotic models.