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arXiv · 2004.08706

Entanglement revivals as a probe of scrambling in finite quantum systems

Ranjan Modak·Vincenzo Alba·Pasquale Calabrese
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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.

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Ranjan Modak, Vincenzo Alba, Pasquale Calabrese. 2020-08-29. Entanglement revivals as a probe of scrambling in finite quantum systems. https://doi.org/10.1088/1742-5468%2Faba9d9

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