{
  "id": "cond-mat/9909143",
  "version": "v1",
  "published": "1999-09-09T22:57:24.000Z",
  "updated": "1999-09-09T22:57:24.000Z",
  "title": "gl(N|N) Super-Current Algebras for Disordered Dirac Fermions in Two Dimensions",
  "authors": [
    "S. Guruswamy",
    "A. LeClair",
    "A. W. W. Ludwig"
  ],
  "comment": "LaTeX, 40 pages",
  "journal": "Nucl.Phys. B583 (2000) 475-512",
  "doi": "10.1016/S0550-3213(00)00245-5",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.dis-nn",
    "cond-mat.stat-mech",
    "hep-th"
  ],
  "abstract": "We consider the non-hermitian 2D Dirac Hamiltonian with (A): real random mass, imaginary scalar potential and imaginary gauge field potentials, and (B) arbitrary complex random potentials of all three kinds. In both cases this Hamiltonian gives rise to a delocalization transition at zero energy with particle-hole symmetry in every realization of disorder. Case (A) is in addition time-reversal invariant, and can also be interpreted as the random-field XY Statistical Mechanics model in two dimensions. The supersymmetric approach to disorder averaging results in current-current perturbations of $gl(N|N)$ super-current algebras. Special properties of the $gl(N|N)$ algebra allow the exact computation of the beta-functions, and of the correlation functions of all currents. One of them is the Edwards-Anderson order parameter. The theory is `nearly conformal' and possesses a scale-invariant subsector which is not a current algebra. For N=1, in addition, we obtain an exact solution of all correlation functions. We also study the delocalization transition of case (B), with broken time reversal symmetry, in the Gade-Wegner (Random-Flux) universality class, using a GL(N|N;C)/U(N|N) sigma model, as well as its PSL(N|N) variant, and a corresponding generalized random XY model. For N=1 the sigma model is shown to be identical to the current-current perturbation. For the delocalization transitions (case (A) and (B)) a density of states, diverging at zero energy, is found.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-09-09T22:57:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "disordered dirac fermions",
      "super-current algebras",
      "generalized random xy model",
      "xy statistical mechanics model",
      "delocalization transition"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier",
      "journal": "Nucl. Phys. B"
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 506923
    }
  }
}