A random matrix model with localization and ergodic transitions

2015/08/31 by V. E. Kravtsov, I. M. Khaymovich, E. Cuevas +1 · 2 citations
Physics and Astronomy · #cond-mat.dis-nn

paper · pdf · doi:10.1088/1367-2630/17/12/122002

published as New Journal of Physics 17, 122002 (2015) · 8 pages, 9 figures (main text) + 7 pages, 4 figures (supplementary materials)

arxiv created 2015/12/28 · arxiv updated 2015/12/29

Abstract

Motivated by the problem of Many-Body Localization and the recent numerical results for the level and eigenfunction statistics on the random regular graphs, a generalization of the Rosenzweig-Porter random matrix model is suggested that possesses two localization transitions as the parameter γ of the model varies from 0 to ∞. One of them is the Anderson transition from the localized to the extended states that happens at γ=2. The other one at γ=1 is the transition from the extended non-ergodic (multifractal) states to the extended ergodic states similar to the eigenstates of the Gaussian Orthogonal Ensemble. We computed the two-level spectral correlation function, the spectrum of multifractality f(α) and the wave function overlap which all show the transitions at γ=1 and γ=2.

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