{
  "id": "1508.07293",
  "version": "v1",
  "published": "2015-08-28T17:52:06.000Z",
  "updated": "2015-08-28T17:52:06.000Z",
  "title": "Spectral statistics across the many-body localization transition",
  "authors": [
    "Maksym Serbyn",
    "Joel E. Moore"
  ],
  "comment": "5 pages, 3 figures",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech",
    "quant-ph"
  ],
  "abstract": "The many-body localization transition (MBLT) between ergodic and many-body localized phase in disordered interacting systems is a subject of much recent interest. Statistics of eigenenergies is known to be a powerful probe of crossovers between ergodic and integrable systems in simpler examples of quantum chaos. We consider the evolution of the spectral statistics across the MBLT, starting with mapping to a Brownian motion process that analytically relates the spectral properties to the statistics of matrix elements. We demonstrate that the flow from Wigner-Dyson to Poisson statistics is a two-stage process. First, fractal enhancement of matrix elements upon approaching the MBLT from the metallic side produces an effective power-law interaction between energy levels, and leads to a plasma model for level statistics. At the second stage, the gas of eigenvalues has local interaction and level statistics belongs to a semi-Poisson universality class. We verify our findings numerically on the XXZ spin chain. We provide a microscopic understanding of the level statistics across the MBLT and discuss implications for the transition that are strong constraints on possible theories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-28T17:52:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "many-body localization transition",
      "spectral statistics",
      "matrix elements",
      "metallic side produces",
      "brownian motion process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}