Rigorous and simple results on very slow thermalization, or quasi-localization, of the disordered quantum chain

Abstract

This paper originates from lectures delivered at the summer school “Fundamental Problems in Statistical Physics XV” in Bruneck, Italy, in 2021. We give a brief and limited introduction into ergodicity-breaking induced by disorder. As the title suggests, we include a simple yet rigorous and original result: For a strongly disordered quantum chain, we exhibit a full set of quasi-local quantities whose dynamics is negligible up to times of order exp{c(logW)2−ϵ}, with ϵ<1, c a numerical constant, and W the disorder strength. Such a result, that is often referred to as “quasi-localization”, can in principle be obtained in other systems as well, but for a disordered quantum chain, its proof is relatively short and transparent.