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

Journal Article · Wed Dec 15 04:00:00 EST 2021 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2021.168525· OSTI ID:23183167

Mirlin, A. D. ^[1]

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1. Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76021 Karlsruhe (Germany)

Highlights: • 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. 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.

• OSTI ID: 23183167
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 435; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CORRELATION FUNCTIONS
EIGENFUNCTIONS
EIGENSTATES
ENERGY LEVELS
FRACTALS
MANY-BODY PROBLEM
QUANTUM DOTS
RANDOMNESS
SPIN