The Ergodic Side of the Many-Body Localization Transition

Abstract

Recent studies point towards nontriviality of the ergodic phase in systems exhibiting many-body localization (MBL), which shows subexponential relaxation of local observables, subdiffusive transport and sublinear spreading of the entanglement entropy. Here we review the dynamical properties of this phase and the available numerically exact and approximate methods for its study. We discuss in which sense this phase could be considered ergodic and present possible phenomenological explanations of its dynamical properties. We close by analyzing to which extent the proposed explanations were verified by numerical studies and present the open questions in this field.

Review article (25 pages, 2 figures). Adds missing references to the Appendix on the relation between the mean-square displacement and the current-current correlation functions