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arXiv · 1508.01714

A random matrix model with localization and ergodic transitions

V. E. Kravtsov·I. M. Khaymovich·E. Cuevas·M. Amini
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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 $\gamma$ of the model varies from 0 to $\infty$. One of them is the Anderson transition from the localized to the extended states that happens at $\gamma=2$. The other one at $\gamma=1$ 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 $f(\alpha)$ and the wave function overlap which all show the transitions at $\gamma=1$ and $\gamma=2$.

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V. E. Kravtsov, I. M. Khaymovich, E. Cuevas, M. Amini. 2015-08-07. A random matrix model with localization and ergodic transitions. https://doi.org/10.1088/1367-2630/17/12/122002

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