Title: Many-Body Localization

Abstract: I will discuss the state of affairs on the topic of many-body localization (MBL).  For the sake of this talk, MBL is defined as a robust absence of transport in many-body systems at thermodynamic parameters corresponding to non-zero entropy density, ie. for example, excluding systems near the ground state.   First, I will present theoretical considerations and numerics that point to the conclusion that MBL is a rather marginal phenomenon: it is restricted to strongly disordered one-dimensional systems with finite on-site space. This finding is still a topic of ongoing debate.   If time permits, I will also present another point of view: we can give up on strict absence of transport and we investigate occurrence of slow transport and thermalization. Here slow means ‘non-perturbative in some parameter’, i.e. due to instanton effects. This phenomenon, that is sometimes also called ‘asymptotic localization’ or ‘quasi-localization’ or simply also ‘MBL’ occurs in much greater generality and it is easily amenable to rigorous mathematical analysis.

Talk – Video

Talk – Slides