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arXiv · 1901.10502

Sub-ballistic growth of R\'enyi entropies due to diffusion

Tibor Rakovszky·Frank Pollmann·C. W. von Keyserlingk
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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 R\'enyi entropies. We argue that the latter generically grow \emph{sub-ballistically}, as $\propto\sqrt{t}$, in systems with diffusive transport. We provide strong evidence for this in both a U$(1)$ symmetric random circuit model and in a paradigmatic non-integrable 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 R\'enyi entropy and show that it exhibits hydrodynamic tails with \emph{three distinct power laws} occurring for different classes of initial states.

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Tibor Rakovszky, Frank Pollmann, C. W. von Keyserlingk. 2019-01-29. Sub-ballistic growth of R\'enyi entropies due to diffusion. https://doi.org/10.1103/physrevlett.122.250602

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