Extended nonergodic states in disordered many‐body quantum systems

This work supports the existence of extended nonergodic states in the intermediate region between the chaotic (thermal) and the many‐body localized phases. These states are identified through an extensive analysis of static and dynamical properties of a finite one‐dimensional system with onsite random disorder. The long‐time dynamics is particularly sensitive to changes in the spectrum and in the structures of the eigenstates. The study of the evolution of the survival probability, Shannon information entropy, and von Neumann entanglement entropy enables the distinction between the chaotic and the intermediate region. Despite the consensus that the transition from a metal to an insulator can still take place in quantum systems with many interacting particles, the details are not entirely understood. It has been debated, for instance, whether there is an intermediate phase between the chaotic and the many‐body localized phase. Our results for the long‐time evolution of the survival probability makes clear the existence of the intermediate region.