Renormalization group analysis of the Anderson model on random regular graphs

• 成果类型: Article
• 署名作者: Vanoni, Carlo; Altshuler, Boris; Kravtsovd, Vladimir E.; Scardicchiob, Antonello
• 署名单位: International School for Advanced Studies (SISSA); Istituto Nazionale di Fisica Nucleare (INFN); Columbia University; Abdus Salam International Centre for Theoretical Physics (ICTP)
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-11357
• DOI: 10.1073/pnas.2401955121
• 发表日期: 2024-07-16
• 关键词: continuous symmetry group; quasi-particle lifetime; long-range order; bethe lattice; localization transition; 2-dimensional systems; spin-glass; quantum; destruction; diffusion

摘要

We present a renormalization group (RG) analysis of the problem of Anderson localization on a random regular graph (RRG) which generalizes the RG of Abrahams, Anderson, Licciardello, and Ramakrishnan to infinite-dimensional graphs. The RG equations necessarily involve two parameters (one being the changing connectivity of subtrees), but we show that the one-parameter scaling hypothesis is recovered for sufficiently large system sizes for both eigenstates and spectrum observables. We also explain the nonmonotonic behavior of dynamical and spectral quantities as a function of the system size for values of disorder close to the transition, by identifying two terms in the beta function of the running fractal dimension of different signs and functional dependence. Our theory provides a simple and coherent explanation for the unusual scaling behavior observed in numerical data of the Anderson model on RRG and of many-body localization.