Sub-ballistic growth of R\'enyi entropies due to diffusion
| Autor: | Rakovszky, Tibor, Pollmann, Frank, von Keyserlingk, C. W. |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Phys. Rev. Lett. 122, 250602 (2019) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevLett.122.250602 |
| Popis: | 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. Comment: close to published version: 4 + epsilon pages, 3 figures + supplement |
| Databáze: | arXiv |
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