1997/02/28 by Alexander D. Mirlin, Yan V. Fyodorov · 5 citations
Chemistry · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Quantum and electron transport phenomena #Quantum many-body systems #cond-mat.dis-nn #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.56.13393
published as Phys. Rev. B 56, 13393 (1997) · 12 pages, 1 figure. Misprints in eqs.(21) and (28) corrected, section VII added. Accepted for publication in Phys. Rev. B
arxiv created 1997/08/26 · openalex publication_date 1997/11/15 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We study fluctuations of the local density of states (LDOS) on a treelike lattice with large branching number m. The average form of the local spectral function (at a given value of the random potential in the observation point) shows a crossover from the Lorentzian to a semicircular form at \ensuremathα\ensuremath∼1/m, where \ensuremathα=(V/W)2, V is the typical value of the hopping matrix element, and W is the width of the distribution of random site energies. For \ensuremathα>1/m2 the LDOS fluctuations (with respect to this average form) are weak. In the opposite case \ensuremathα<1/m2, the fluctuations become strong and the average LDOS ceases to be representative, which is related to the existence of the Anderson transition at \ensuremathαc\ensuremath∼1/m2log2m. On the localized side of the transition the spectrum is discrete and the LDOS is given by a set of \ensuremathδ-like peaks. The effective number of components in this regime is given by 1/P, with P being the inverse participation ratio. It is shown that P has in the transition point a limiting value Pc close to unity, 1\ensuremath-Pc\ensuremath∼1/logm, so that the system undergoes a transition directly from the deeply localized phase to the extended phase. On the side of delocalized states, the peaks in the LDOS become broadened, with a width \ensuremath∼exp\ensuremath-constlogm[(\ensuremathα\ensuremath-\ensuremathαc)/\ensuremathαc]^\ensuremath-1/2 being exponentially small near the transition point. We discuss the application of our results to the problem of the quasiparticle line shape in a finite Fermi system, as suggested recently by Altshuler, Gefen, Kamenev, and Levitov [Phys. Rev. Lett. 78, 2803 (1997)].