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

Sarang Gopalakrishnan

David A. Huse

  • Department of Physics and Astronomy, CUNY College of Staten Island, Staten Island, New York 10314, USA and Physics Program and Initiative for Theoretical Sciences, CUNY Graduate Center, New York, New York 10016, USA

  • Department of Physics, Princeton University, Princeton, New Jersey 08544, USA

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Phys. Rev. B 99, 134305 – Published 16 April, 2019

DOI: https://doi.org/10.1103/PhysRevB.99.134305

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.

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Phys. Rev. B 99, 134305– Published 16 April, 2019
  • Received 24 January 2019
Article part of CHORUS
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