Sub-ballistic growth of Rényi Entropies due to diffusion

T. Rakovszky, F. Pollmann, C.W. Von Keyserlingk

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26 Citations (Scopus)
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Abstract

We investigate the dynamics of quantum entanglement after a global quench and uncover a qualitative difference between the behavior of the von Neumann entropy and higher Rényi entropies. We argue that the latter generically grow sub-ballistically, as ∝√t, in systems with diffusive transport. We provide strong evidence for this in both a U(1) symmetric random circuit model and in a paradigmatic nonintegrable spin chain, where energy is the sole conserved quantity. We interpret our results as a consequence of local quantum fluctuations in conserved densities, whose behavior is controlled by diffusion, and use the random circuit model to derive an effective description. We also discuss the late-time behavior of the second Rényi entropy and show that it exhibits hydrodynamic tails with three distinct power laws occurring for different classes of initial states.
Original languageEnglish
Article number250602
Number of pages6
JournalPhysical Review Letters
Volume122
Issue number25
Early online date25 Jun 2019
DOIs
Publication statusPublished - 28 Jun 2019

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