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Localization as an Entanglement Phase Transition in Boundary-Driven Anderson Models

Author(s): Gullans, Michael J; Huse, David A

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Abstract: The Anderson localization transition is one of the most well studied examples of a zero temperature quantum phase transition. On the other hand, many open questions remain about the phenomenology of disordered systems driven far out of equilibrium. Here we study the localization transition in the prototypical three-dimensional, noninteracting Anderson model when the system is driven at its boundaries to induce a current carrying nonequilibrium steady state. Recently we showed that the diffusive phase of this model exhibits extensive mutual information of its nonequilibrium steady-state density matrix. We show that this extensive scaling persists in the entanglement and at the localization critical point, before crossing over to a short-range (area-law) scaling in the localized phase. We introduce an entanglement witness for fermionic states that we name the mutual coherence, which, for fermionic Gaussian states, is also a lower bound on the mutual information. Through a combination of analytical arguments and numerics, we determine the finite-size scaling of the mutual coherence across the transition. These results further develop the notion of entanglement phase transitions in open systems, with direct implications for driven many-body localized systems, as well as experimental studies of driven-disordered systems.
Publication Date: 13-Sep-2019
Electronic Publication Date: 10-Sep-2019
Citation: Gullans, Michael J, Huse, David A. (2019). Localization as an Entanglement Phase Transition in Boundary-Driven Anderson Models. PHYSICAL REVIEW LETTERS, 123 (10.1103/PhysRevLett.123.110601
DOI: doi:10.1103/PhysRevLett.123.110601
ISSN: 0031-9007
EISSN: 1079-7114
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW LETTERS
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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