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Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit

Author(s): Gopalakrishnan, Sarang; Huse, David A

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Abstract: The many-body localization (MBL) phase transition is not a conventional thermodynamic phase transition. Thus, to define the phase transition, one should allow the possibility of taking the limit of an infinite system in a way that is not the conventional thermodynamic limit. We explore this for the so-called avalanche instability due to rare thermalizing regions in the MBL phase for systems with quenched randomness in two cases: for short-range interacting systems in more than one spatial dimension and for systems in which the interactions fall off with distance as a power law. We find an unconventional way of scaling these systems so that they do have a type of phase transition. Our arguments suggest that the MBL phase transition in systems with short-range interactions in more than one dimension (or with sufficiently rapidly decaying power laws) is a transition where entanglement in the eigenstates begins to spread into some typical regions: The transition is set by when the avalanches start. Once this entanglement gets started, the system does thermalize. From this point of view, the much-studied case of one-dimensional MBL with short-range interactions is a special case with a different, and in some ways more conventional, type of phase transition.
Publication Date: Apr-2019
Electronic Publication Date: 16-Apr-2019
Citation: Gopalakrishnan, Sarang, Huse, David A. (2019). Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit. PHYSICAL REVIEW B, 99 (10.1103/PhysRevB.99.134305
DOI: doi:10.1103/PhysRevB.99.134305
ISSN: 2469-9950
EISSN: 2469-9969
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW B
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.

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