Extensive entropy from unitary evolution

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)].

References in corpus (5)

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• Phenomenology of fully many-body-localized systems
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• A Sharp Fannes-type Inequality for the von Neumann Entropy
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Cited by in corpus (5)

• Many-Body Localization in the Age of Classical Computing
• Simulating a measurement-induced phase transition for trapped ion circuits
• 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