From Anderson localization on Random Regular Graphs to Many-Body localization
Disordered Systems and Neural Networks
2021-10-15 v1
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.
Cite
@article{arxiv.2102.05930,
title = {From Anderson localization on Random Regular Graphs to Many-Body localization},
author = {K. S. Tikhonov and A. D. Mirlin},
journal= {arXiv preprint arXiv:2102.05930},
year = {2021}
}