Extensive entropy from unitary evolution

• URL: http://arxiv.org/abs/2104.02053v1
• Date: Mon, 5 Apr 2021 17:59:16 GMT
• Title: Extensive entropy from unitary evolution
• Authors: Yichen Huang
• Abstract summary: In quantum many-body systems, a Hamiltonian is called an extensive entropy generator'' 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.
• Score: 2.741266294612776
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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