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arXiv · 2102.05930

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

K. S. Tikhonov·A. D. Mirlin
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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.

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K. S. Tikhonov, A. D. Mirlin. 2021-02-11. From Anderson localization on Random Regular Graphs to Many-Body localization. https://doi.org/10.1016/j.aop.2021.168525

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