Extensive entropy from unitary evolution
arXiv:2104.02053 · doi:10.20944/preprints202104.0254.v1 10.12351/ks.2109.0928
Abstract
In quantum many-body systems, a Hamiltonian is called an ``extensive entropy generator'' if starting from a random product state the entanglement entropy obeys a volume law at long times with overwhelming probability. We prove that (i) any Hamiltonian whose spectrum has non-degenerate gaps is an extensive entropy generator; (ii) in the space of (geometrically) local Hamiltonians, the non-degenerate gap condition is satisfied almost everywhere. Specializing to many-body localized systems, these results imply the observation stated in the title of Bardarson et al. [PRL 109, 017202 (2012)].
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- Many-Body Localization in the Age of Classical Computing
- Simulating a measurement-induced phase transition for trapped ion circuits
- Scaling properties of a spatial one-particle density-matrix entropy in many-body localized systems
- Entanglement Dynamics From Random Product States: Deviation From Maximal Entanglement
- Quantum thermalization must occur in translation-invariant systems at high temperature
- Long-time properties of generic Floquet systems are approximately periodic with the driving period