The Ergodic Side of the Many-Body Localization Transition

TL;DR

This paper reviews the nontrivial ergodic phase in many-body localized systems, focusing on its dynamical properties, numerical methods for study, and the ongoing debate about its ergodicity and underlying mechanisms.

Contribution

It provides a comprehensive review of the dynamical behavior of the ergodic phase in MBL systems and discusses the validity of phenomenological explanations supported by numerical evidence.

Findings

Subexponential relaxation of local observables

Subdiffusive transport in the ergodic phase

Sublinear entanglement spreading

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.