Dynamics of many-body localized systems: logarithmic lightcones and $\log \, t$-law of $\alpha$-Rényi entropies
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$-Rényi 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.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2024
- DOI:
- 10.48550/arXiv.2408.02016
- arXiv:
- arXiv:2408.02016
- Bibcode:
- 2024arXiv240802016T
- Keywords:
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- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Mesoscale and Nanoscale Physics;
- Mathematical Physics;
- Quantum Physics
- E-Print:
- 12 pages plus references