From Anderson localization on random regular graphs to many-body localization

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 discu...

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Bibliographic Details
Published in:Annals of physics 2021-12, Vol.435, p.168525, Article 168525
Main Authors: Tikhonov, K.S., Mirlin, A.D.
Format: Article
Language:English
Subjects:
Anderson localization
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CORRELATION FUNCTIONS
Critical behavior
Eigenfunction statistics
EIGENFUNCTIONS
EIGENSTATES
Energy level statistics
ENERGY LEVELS
Ergodicity
FRACTALS
Many-body localization
MANY-BODY PROBLEM
MATERIALS SCIENCE
QUANTUM DOTS
Random regular graph
RANDOMNESS
SPIN
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Summary: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. •Anderson transition from ergodicity to localization on random regular graphs (RRG).•Analytical, pool method, and exact-diagonalization study of correlations on RRG.•Many-body localization (MBL) to ergodicity transition: quantum dots and spin chains.•Dynamical eigenstate correlation functions in RRG and MBL problems.•Anderson localization on RRG as a toy model for MBL.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2021.168525