Renormalization group for Anderson localization on high-dimensional lattices

• 成果类型: Article
• 署名作者: Altshuler, Boris L.; Kravtsov, Vladimir E.; Scardicchio, Antonello; Sierant, Piotr; Vanoni, Carlo
• 署名单位: Columbia University; Abdus Salam International Centre for Theoretical Physics (ICTP); Istituto Nazionale di Fisica Nucleare (INFN); Barcelona Institute of Science & Technology; Universitat Politecnica de Catalunya; Institut de Ciencies Fotoniques (ICFO); International School for Advanced Studies (SISSA)
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-13536
• DOI: 10.1073/pnas.2423763122
• 发表日期: 2025-09-02
• 关键词: nonlinear sigma-model; self-consistent theory; eigenfunction correlations; mesoscopic fluctuations; diffusion; TRANSITION; absence; SYSTEM; phase

摘要

We discuss the dependence of the critical properties of the Anderson model on the dimension d in the language of /3-function and renormalization group recently introduced in Vanoni et al. [C. Vanoni et al., Proc. Natl. Acad. Sci. U.S.A. 121, e2401955121 (2024)] in the context of Anderson transition on random regular graphs. We show how in the delocalized region, including the transition point, the one-parameter scaling part of the /3-function for the fractal dimension D1 evolves smoothly from its d = 2 form, in which /32 <= 0, to its i infinity >= 0 form, which is represented by the random regular graph (RRG) result. We show how the e = d-2 expansion and the 1/d expansion around the RRG result can be reconciled and how the initial part of a renormalization group trajectory governed by the irrelevant exponent y depends on dimensionality. We also show how the irrelevant exponent emerges out of the high-gradient terms of expansion in the nonlinear sigma model and put forward a conjecture about a lower bound for the fractal dimension. The framework introduced here may serve as a basis for investigations of disordered many-body systems and of more general nonequilibrium quantum systems.