Lydia Giacomin

Localization in certain disordered quantum spin chains.

The phenomenon of localization in disordered systems was first described by Philip W. Anderson, who highlighted the insulating behavior that certain single-particle lattice models display in the presence of strong disorder. Since then, localization phenomena have been studied in depth. While Anderson localization is well-understood at strong disorder (with mathematical proofs achieved for any dimension), the question whether or not Anderson insulators retain localization properties in the presence of interactions remains open. In this talk, I will present an overview of the current scope of knowledge on this topic (known as many-body localization, or MBL) and highlight a recent result which aims to set a rigorous mathematical framework for the proof of MBL. Using a multi-scale analysis, one can show absence of diffusion for a robust set of interacting 1D spin chain models. The reasoning leading to this result can be extended to hopefully derive a rigorous proof of MBL, an aspect that is left for further work.

Joint work with Wojciech De Roeck, Francois Huveneers and Oskar Prosniak – based on prior work by John Z. Imbrie.