{
  "id": "1001.2984",
  "version": "v2",
  "published": "2010-01-18T09:21:16.000Z",
  "updated": "2010-03-29T14:46:25.000Z",
  "title": "Many-body localization transition in a lattice model of interacting fermions: statistics of renormalized hoppings in configuration space",
  "authors": [
    "Cecile Monthus",
    "Thomas Garel"
  ],
  "comment": "v2 revised version with new material on real-space correlation (11 pages, 11 figures)",
  "journal": "Phys. Rev. B 81, 134202 (2010)",
  "doi": "10.1103/PhysRevB.81.134202",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.str-el"
  ],
  "abstract": "We consider the one-dimensional lattice model of interacting fermions with disorder studied previously by Oganesyan and Huse [Phys. Rev. B 75, 155111 (2007)]. To characterize a possible many-body localization transition as a function of the disorder strength $W$, we use an exact renormalization procedure in configuration space that generalizes the Aoki real-space RG procedure for Anderson localization one-particle models [H. Aoki, J. Phys. C13, 3369 (1980)]. We focus on the statistical properties of the renormalized hopping $V_L$ between two configurations separated by a distance $L$ in configuration space (distance being defined as the minimal number of elementary moves to go from one configuration to the other). Our numerical results point towards the existence of a many-body localization transition at a finite disorder strength $W_c$. In the localized phase $W>W_c$, the typical renormalized hopping $V_L^{typ} \\equiv e^{\\bar{\\ln V_L}}$ decays exponentially in $L$ as $ (\\ln V_L^{typ}) \\simeq - \\frac{L}{\\xi_{loc}}$ and the localization length diverges as $\\xi_{loc}(W) \\sim (W-W_c)^{-\\nu_{loc}}$ with a critical exponent of order $\\nu_{loc} \\simeq 0.5$. In the delocalized phase $W<W_c$, the renormalized hopping remains a finite random variable as $L \\to \\infty$, and the typical asymptotic value $V_{\\infty}^{typ} \\equiv e^{\\bar{\\ln V_{\\infty}}}$ presents an essential singularity $(\\ln V_{\\infty}^{typ}) \\sim - (W_c-W)^{-\\kappa}$ with an exponent of order $\\kappa \\sim 1.4$. Finally, we show that this analysis in configuration space is compatible with the localization properties of the simplest two-point correlation function in real space.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-03-29T14:46:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "71.30.+h",
      "71.23.An",
      "72.15.Rn"
    ],
    "keywords": [
      "many-body localization transition",
      "configuration space",
      "renormalized hopping",
      "lattice model",
      "interacting fermions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review B",
      "year": 2010,
      "month": "Apr",
      "volume": 81,
      "number": 13,
      "pages": 134202
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010PhRvB..81m4202M"
    }
  }
}