Many-Body (De-)Localization - Status and Perspectives

Anderson localization is a quantum-interference phenomenon that turns disordered wires into isulators. The fate of Anderson-localization in the presence of many-body interactions received considerable attention over the past twenty years within the field of condensed matter physics and beyond. Early work proclaimed many-body localization (MBL): particles remain strictly localized at strong enough disorder. In stark contrast, extensive computational studies demonstrated recently the absence of MBL in the MBL-fruit-fly model, the random field Heisenberg chain. Despite many claims to the opposite, many-body delocalization (MBdL) prevails in the numerically accessible parameter window. Most recent investigations uncover further details of the relaxation dynamics: MBdL exhibits a surprising degree of universality when adopting the entanglement evolution as a measure of time. The observation motivates us to introduce the "internal clock" as a novel concept for describing systems with slow relaxation dynamics. The talk will describe the state of affairs in MBL and offer a perspective on future developments.