Extensive entropy from unitary evolution
Quantum Physics
2021-11-08 v1 Disordered Systems and Neural Networks
Statistical Mechanics
Mathematical Physics
math.MP
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)].
Cite
@article{arxiv.2104.02053,
title = {Extensive entropy from unitary evolution},
author = {Yichen Huang},
journal= {arXiv preprint arXiv:2104.02053},
year = {2021}
}