{
  "id": "1508.01714",
  "version": "v1",
  "published": "2015-08-07T14:54:54.000Z",
  "updated": "2015-08-07T14:54:54.000Z",
  "title": "A random matrix model with two localization transitions",
  "authors": [
    "V. E. Kravtsov",
    "I. M. Khaymovich",
    "E. Cuevas",
    "M. Amini"
  ],
  "comment": "5 pages, 4 figures (main text) + 8 pages, 10 figures (supplementary materials)",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "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 $\\gamma=2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-07T14:54:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "localization transitions",
      "two-level spectral correlation function",
      "rosenzweig-porter random matrix model",
      "extended ergodic states similar",
      "wave function overlap"
    ],
    "publication": {
      "doi": "10.1088/1367-2630/17/12/122002",
      "journal": "New Journal of Physics",
      "year": 2015,
      "month": "Dec",
      "volume": 17,
      "number": 12,
      "pages": 122002
    },
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015NJPh...17l2002K"
    }
  }
}