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Preserved in Portico This version is not peer-reviewed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. https://doi.org/10.20944/preprints202104.0254.v1 Huang, Y. Extensive Entropy from Unitary Evolution. Preprints 2021, 2021040254. https://doi.org/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)].
Keywords
entanglement entropy; local Hamiltonian; many-body localization; quantum dynamics; volume law
Subject
Physical Sciences, Mathematical Physics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment