{
  "id": "cond-mat/0501246",
  "version": "v1",
  "published": "2005-01-11T11:56:35.000Z",
  "updated": "2005-01-11T11:56:35.000Z",
  "title": "Real-space renormalization-group approach to the integer quantum Hall effect",
  "authors": [
    "Philipp Cain",
    "Rudolf A. Roemer"
  ],
  "comment": "35 pages, 14 figures, submitted to Int. J. Mod. Phys. B",
  "journal": "Int. J. Mod. Phys. B 19, 2085-2119 (2005)",
  "doi": "10.1142/S0217979205029742",
  "categories": [
    "cond-mat.mes-hall"
  ],
  "abstract": "We review recent results based on an application of the real-space renormalization group (RG) approach to a network model for the integer quantum Hall (QH) transition. We demonstrate that this RG approach reproduces the critical distribution of the power transmission coefficients, i.e., two-terminal conductances, P_c(G), with very high accuracy. The RG flow of P(G) yields a value of the critical exponent nu that agrees with most accurate large-size lattice simulations. A description of how to obtain other relevant transport coefficients such as R_L and R_H is given. From the non-trivial fixed point of the RG flow we extract the critical level-spacing distribution (LSD) which is close, but distinctively different from the earlier large-scale simulations. We find that the LSD obeys scaling behavior around the QH transition with nu=2.37\\pm 0.02. Away from the transition it changes towards the Poisson distribution. We next investigate the plateau-to-insulator transition. For a fully quantum coherent situation, we find a quantized Hall insulator with R_H ~ h/e^2 up to R_L ~ 20 h/e^2 when interpreting the results in terms of the most probable value of the distribution P(R_H). Upon further increasing R_L, the Hall insulator with diverging R_H ~ R_L^kappa is seen. This crossover depends on the precise nature of the averaging of P(R_L) and P(R_H). We also study the effect of long-ranged inhomogeneities on the critical properties of the QH transition modeled by a power law correlation in the random potential. Similar to the classical percolation, we observe an enhancement of nu with decreasing correlation range. These results exemplify the surprising fact that a small RG unit, containing five nodes, accurately captures most of the correlations responsible for the QH transition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-01-11T11:56:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integer quantum hall effect",
      "real-space renormalization-group approach",
      "qh transition",
      "distribution",
      "rg flow"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "International Journal of Modern Physics B",
      "year": 2005,
      "volume": 19,
      "number": 13,
      "pages": 2085
    },
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005IJMPB..19.2085C"
    }
  }
}