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arXiv · 2104.02053

Extensive entropy from unitary evolution

Yichen Huang
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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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Yichen Huang. 2021-04-05. Extensive entropy from unitary evolution. https://doi.org/10.20944/preprints202104.0254.v1 10.12351/ks.2109.0928

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