2017/08/31 by Michael Sonner, M. Sonner, K. S. Tikhonov +1
Mathematics · Physics and Astronomy · #Anderson localization #Bethe lattice #Delocalized electron #Eigenfunction #Eigenvalues and eigenvectors #Fractal #Geometry #Lattice (music) #Mathematical analysis #Mathematical physics #Mathematics #Multifractal system #Opinion Dynamics and Social Influence #Physics #Physics of Superconductivity and Magnetism #Quantum many-body systems #Quantum mechanics #Scaling #Statistical physics #Wave function #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevb.96.214204
published as Phys. Rev. B 96, 214204 (2017)
openalex publication_date 2017/12/20 · arxiv created 2017/12/23 · arxiv updated 2017/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Disordered quantum systems undergo Anderson localization-delocalization transitions, which exhibit very rich physics. A remarkable feature of these transitions is the multifractality of critical wave functions. The eigenfunction multifractality in a d-dimensional disordered system holds only at the transition point and is characterized by universal critical exponents. The authors explore the evolution of wave-function statistics on a finite Bethe lattice from the central site (``root'') to the boundary (``leaves''). They show that eigenfunction moments exhibit generally a multifractal scaling with the volume N. The multifractality spectrum \ensuremathτq depends on the disorder strength and on the parameter s characterizing the position of the observation point, s = r/R, where r is the distance to the root and R is the ``radius'' of the lattice.