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

K. S. Tikhonov, A. D. Mirlin

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

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.

Original languageEnglish
Article number168525
JournalAnnals of Physics
Volume435
DOIs
Publication statusPublished - Dec 2021

Keywords

  • Anderson localization
  • Critical behavior
  • Eigenfunction statistics
  • Energy level statistics
  • Ergodicity
  • Many-body localization
  • Random regular graph

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