Dynamics of many-body localized systems: logarithmic lightcones and $\log \, t$-law of $α$-Rényi entropies

• URL: http://arxiv.org/abs/2408.02016v1
• Date: Sun, 4 Aug 2024 12:53:55 GMT
• Title: Dynamics of many-body localized systems: logarithmic lightcones and $\log \, t$-law of $α$-Rényi entropies
• Authors: Daniele Toniolo, Sougato Bose,
• Abstract summary: We evaluate the dynamical generation of $ alpha$-R'enyi entropies, $ 0 alpha1 $ close to one, obtaining a $log, t$-law. We show that the dynamical generation of the von Neumann entropy, from a generic initial product state, has for large times a $ log, t$-shape.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the context of the Many-Body-Localization phenomenology we consider arbitrarily large one-dimensional spin systems. The XXZ model with disorder is a prototypical example. Without assuming the existence of exponentially localized integrals of motion (LIOMs), but assuming instead a logarithmic lightcone we rigorously evaluate the dynamical generation of $ \alpha$-R\'enyi entropies, $ 0< \alpha<1 $ close to one, obtaining a $\log \, t$-law. Assuming the existence of LIOMs we prove that the Lieb-Robinson (L-R) bound of the system's dynamics has a logarithmic lightcone and show that the dynamical generation of the von Neumann entropy, from a generic initial product state, has for large times a $ \log \, t$-shape. L-R bounds, that quantify the dynamical spreading of local operators, may be easier to measure in experiments in comparison to global quantities such as entanglement.

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