--- res: bibo_abstract: - We propose a scaling theory for the many-body localization (MBL) phase transition in one dimension, building on the idea that it proceeds via a “quantum avalanche.” We argue that the critical properties can be captured at a coarse-grained level by a Kosterlitz-Thouless (KT) renormalization group (RG) flow. On phenomenological grounds, we identify the scaling variables as the density of thermal regions and the length scale that controls the decay of typical matrix elements. Within this KT picture, the MBL phase is a line of fixed points that terminates at the delocalization transition. We discuss two possible scenarios distinguished by the distribution of rare, fractal thermal inclusions within the MBL phase. In the first scenario, these regions have a stretched exponential distribution in the MBL phase. In the second scenario, the near-critical MBL phase hosts rare thermal regions that are power-law-distributed in size. This points to the existence of a second transition within the MBL phase, at which these power laws change to the stretched exponential form expected at strong disorder. We numerically simulate two different phenomenological RGs previously proposed to describe the MBL transition. Both RGs display a universal power-law length distribution of thermal regions at the transition with a critical exponent αc=2, and continuously varying exponents in the MBL phase consistent with the KT picture.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Philipp T. foaf_name: Dumitrescu, Philipp T. foaf_surname: Dumitrescu - foaf_Person: foaf_givenName: Anna foaf_name: Goremykina, Anna foaf_surname: Goremykina - foaf_Person: foaf_givenName: Siddharth A. foaf_name: Parameswaran, Siddharth A. foaf_surname: Parameswaran - foaf_Person: foaf_givenName: Maksym foaf_name: Serbyn, Maksym foaf_surname: Serbyn foaf_workInfoHomepage: http://www.librecat.org/personId=47809E7E-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-2399-5827 - foaf_Person: foaf_givenName: Romain foaf_name: Vasseur, Romain foaf_surname: Vasseur bibo_doi: 10.1103/physrevb.99.094205 bibo_issue: '9' bibo_volume: 99 dct_date: 2019^xs_gYear dct_identifier: - UT:000462883200001 dct_isPartOf: - http://id.crossref.org/issn/2469-9950 - http://id.crossref.org/issn/2469-9969 dct_language: eng dct_publisher: American Physical Society@ dct_title: Kosterlitz-Thouless scaling at many-body localization phase transitions@ ...