2014/03/31 by A. De Luca, Andrea De Luca, B. L. Altshuler +3 · 295 citations
Mathematics · Physics and Astronomy · #Anderson impurity model #Anderson localization #Bethe lattice #Condensed matter physics #Eigenfunction #Eigenvalues and eigenvectors #Equipartition theorem #Ergodicity #Fractal #Impurity #Lattice (music) #Magnetic field #Mathematical physics #Mathematics #Multifractal system #Physics #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Quasiperiodic function #Statistical physics #Topological Materials and Phenomena #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.1103/physrevlett.113.046806
published in Physical Review Letters 113(4), 046806 (American Physical Society) · 5 pages, 3 figures + 4 pages supplemental material. arXiv admin note: text overlap with arXiv:1401.0019
openalex publication_date 2014/07/25 · arxiv created 2014/07/28 · arxiv updated 2014/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Statistical analysis of the eigenfunctions of the Anderson tight-binding model with on-site disorder on regular random graphs strongly suggests that the extended states are multifractal at any finite disorder. The spectrum of fractal dimensions f(α) defined in Eq. (3) remains positive for α noticeably far from 1 even when the disorder is several times weaker than the one which leads to the Anderson localization; i.e., the ergodicity can be reached only in the absence of disorder. The one-particle multifractality on the Bethe lattice signals on a possible inapplicability of the equipartition law to a generic many-body quantum system as long as it remains isolated.