Exploring one-particle orbitals in large many-body localized systems

Abstract

Disorder and interactions can lead to the breakdown of statistical mechanics in quantum systems by transitioning to a many-body localized (MBL) phase. The thermal-to-MBL transition occurs by either increasing the amount of disorder present in a system or by decreasing its energy until it crosses the so-called mobility edge. The authors construct a set of approximate integrals of motion that are quasi-universal across the energy spectrum and, thus, across the mobility edge, too. Interestingly, MBL eigenstates under the mobility edge are aware of the existence of a thermal phase at a higher energy. The phase diagram is probed close to the transition and in the MBL phase. One finds a universal distribution of the strength of the couplings of the integrals of motion in the strong disorder limit.