{
  "id": "0911.5443",
  "version": "v3",
  "published": "2009-11-29T03:09:16.000Z",
  "updated": "2010-07-20T01:26:30.000Z",
  "title": "Conformal invariance, multifractality, and finite-size scaling at Anderson localization transitions in two dimensions",
  "authors": [
    "Hideaki Obuse",
    "Arvind R. Subramaniam",
    "Akira Furusaki",
    "Ilya A. Gruzberg",
    "Andreas W. W. Ludwig"
  ],
  "comment": "13 pages, 7 figures",
  "journal": "Phys. Rev. B 82, 035309 (2010)",
  "doi": "10.1103/PhysRevB.82.035309",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.mes-hall",
    "cond-mat.stat-mech"
  ],
  "abstract": "We generalize universal relations between the multifractal exponent \\alpha_0 for the scaling of the typical wave function magnitude at a (Anderson) localization-delocalization transition in two dimensions and the corresponding critical finite size scaling (FSS) amplitude \\Lambda_c of the typical localization length in quasi-one-dimensional (Q1D) geometry: (i) When open boundary conditions are imposed in the transverse direction of Q1D samples (strip geometry), we show that the corresponding critical FSS amplitude \\Lambda_c^o is universally related to the boundary multifractal exponent \\alpha_0^s for the typical wave function amplitude along a straight boundary (surface). (ii) We further propose a generalization of these universal relations to those symmetry classes whose density of states vanishes at the transition. (iii) We verify our generalized relations [Eqs. (6) and (7)] numerically for the following four types of two-dimensional Anderson transitions: (a) the metal-to-(ordinary insulator) transition in the spin-orbit (symplectic) symmetry class, (b) the metal-to-(Z_2 topological insulator) transition which is also in the spin-orbit (symplectic) class, (c) the integer quantum Hall plateau transition, and (d) the spin quantum Hall plateau transition.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-07-20T01:26:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "73.20.Fz",
      "05.45.Df",
      "72.15.Rn"
    ],
    "keywords": [
      "anderson localization transitions",
      "conformal invariance",
      "finite-size scaling",
      "dimensions",
      "typical wave function"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review B",
      "year": 2010,
      "month": "Jul",
      "volume": 82,
      "number": 3,
      "pages": "035309"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010PhRvB..82c5309O"
    }
  }
}