{
  "id": "1110.6894",
  "version": "v6",
  "published": "2011-10-31T18:43:16.000Z",
  "updated": "2013-04-10T19:37:18.000Z",
  "title": "On the spectrum of 1D quantum Ising quasicrystal",
  "authors": [
    "W. N. Yessen"
  ],
  "comment": "45 pages, 84 references, 14 figures. Final version. To appear in Annal. H. Poincare",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "math.DS",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We consider one dimensional quantum Ising spin-1/2 chains with two-valued nearest neighbor couplings arranged in a quasi-periodic sequence, with uniform, transverse magnetic field. By employing the Jordan-Wigner transformation of the spin operators to spinless fermions, the energy spectrum can be computed exactly on a finite lattice. By employing the transfer matrix technique and investigating the dynamics of the corresponding trace map, we show that in the thermodynamic limit the energy spectrum is a Cantor set of zero Lebesgue measure. Moreover, we show that local Hausdorff dimension is continuous and nonconstant over the spectrum. This forms a rigorous counterpart of numerous numerical studies.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2013-04-10T19:37:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B20",
      "82B44",
      "82D30",
      "82D40",
      "82B10",
      "82B26",
      "82B27"
    ],
    "keywords": [
      "1d quantum ising quasicrystal",
      "energy spectrum",
      "two-valued nearest neighbor couplings",
      "transverse magnetic field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.6894Y"
    }
  }
}