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

Sarang Gopalakrishnan; David A. Huse

doi:10.1103/physrevb.99.134305

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arXiv · 1901.04505

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

Sarang Gopalakrishnan·David A. Huse

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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 quenched-random systems in more than one spatial dimension, finding an unconventional way of scaling the systems so that they do have a type of phase transition. These arguments suggest that the MBL phase transition in systems with short-range interactions in more than one dimension is a transition where entanglement in the eigenstates begins to spread in to 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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Sarang Gopalakrishnan, David A. Huse. 2019-01-14. Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit. https://doi.org/10.1103/physrevb.99.134305

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