Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit
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.
Keywords
Cite
@article{arxiv.1901.04505,
title = {Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit},
author = {Sarang Gopalakrishnan and David A. Huse},
journal= {arXiv preprint arXiv:1901.04505},
year = {2019}
}
Comments
10 pages, 2 figures