Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Extensive Entropy from Unitary Evolution

Version 1 : Received: 8 April 2021 / Approved: 9 April 2021 / Online: 9 April 2021 (10:16:52 CEST)

How to cite: Huang, Y. Extensive Entropy from Unitary Evolution. Preprints 2021, 2021040254 (doi: 10.20944/preprints202104.0254.v1). Huang, Y. Extensive Entropy from Unitary Evolution. Preprints 2021, 2021040254 (doi: 10.20944/preprints202104.0254.v1).

## 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)].

## Subject Areas

entanglement entropy; local Hamiltonian; many-body localization; quantum dynamics; volume law

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