From Anderson localization on Random Regular Graphs to Many-Body localization

TL;DR

This review explores Anderson localization on random regular graphs and its relation to many-body localization, focusing on eigenstate properties, phase transitions, and the effects of interactions in disordered quantum systems.

Contribution

It synthesizes recent insights into the connections between Anderson localization on RRGs and MBL, highlighting common themes and critical phenomena.

Findings

Eigenstate and energy level correlations differ between phases

Localized critical point exhibits unique properties

Finite-size effects are significant in MBL studies

Abstract

The article reviews the physics of Anderson localization on random regular graphs (RRG) and its connections to many-body localization (MBL) in disordered interacting systems. Properties of eigenstate and energy level correlations in delocalized and localized phases, as well at criticality, are discussed. In the many-body part, models with short-range and power-law interactions are considered, as well as the quantum-dot model representing the limit of the "most long-range" interaction. Central themes -- which are common to the RRG and MBL problems -- include ergodicity of the delocalized phase, localized character of the critical point, strong finite-size effects, and fractal scaling of eigenstate correlations in the localized phase.