Seminar for the Leeds-Loughborough-Nottingham Non-Equilibrium Seminars Series
Date:
Title: Renormalization group beta-function for Anderson and many-body localization
Abstract: This talk aims to provide a different viewpoint on localization transitions induced by disorder based on the renormalization group formalism. I will first discuss, on general grounds, the various types of scaling behaviors a localization critical point can display. I will then move to specific models; firstly, I will discuss Anderson localization in finite dimensional space and how one recovers the Anderson model on expander graphs by taking the limit of infinite dimensions. I will then move to many-body localization and show that, if a many-body localized phase exists, the critical point must be described by a two-parameter scaling theory similar to Anderson localization in infinite dimensions and to the BKT transition.
References:
C. Vanoni, B. L. Altshuler, V. E. Kravtsov and A. Scardicchio, Renormalization group analysis of the Anderson model on random regular graphs, PNAS 121 (29) e2401955121 (2024) B. L. Altshuler, V. E. Kravtsov, A. Scardicchio, P. Sierant, and C. Vanoni, Renormalization group for Anderson localization on high-dimensional lattices, arXiv:2403.01974 (2024) F. Balducci, G. Bracci Testasecca, G. Magnifico, J. Niedda, A. Scardicchio and C. Vanoni, Renormalization Group Analysis of the Many-Body Localization transition in the random field XXZ Chain, to appear