{
  "id": "cond-mat/9809228",
  "version": "v3",
  "published": "1998-09-17T06:53:13.000Z",
  "updated": "1999-12-27T06:36:14.000Z",
  "title": "Spectral Gaps of Quantum Hall Systems with Interactions",
  "authors": [
    "Tohru Koma"
  ],
  "comment": "LaTeX, 54 pages, no figures, discussions on periodic potentials and on energy and spatial cutoffs added, typos corrected, accepted for publication in J. Stat. Phys",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.stat-mech"
  ],
  "abstract": "A two-dimensional quantum Hall system without disorder for a wide class of interactions including any two-body interaction with finite range is studied by using the Lieb-Schultz-Mattis method [{\\it Ann. Phys. (N.Y.)} {\\bf 16}: 407 (1961)]. The model is defined on an infinitely long strip with a fixed large width, and the Hilbert space is restricted to the lowest $(n_{\\rm max}+1)$ Landau levels with a large integer $n_{\\rm max}$. We proved that, for a non-integer filling $\\nu$ of the Landau levels, either (i) there is a symmetry breaking at zero temperature or (ii) there is only one infinite-volume ground state with a gapless excitation. We also proved the following two theorems: (a) If a pure infinite-volume ground state has a non-zero excitation gap for a non-integer filling $\\nu$, then a translational symmetry breaking occurs at zero temperature. (b) Suppose that there is no non-translationally invariant infinite-volume ground state. Then, if a pure infinite-volume ground state has a non-zero excitation gap, the filling factor $\\nu$ must be equal to a rational number. Here the ground state is allowed to have a periodic structure which is a consequence of the translational symmetry breaking. We also discuss the relation between our results and the quantized Hall conductance, and phenomenologically explain why odd denominators of filling fractions $\\nu$ giving the quantized Hall conductance, are favored exclusively.",
  "revisions": [
    {
      "version": "v3",
      "updated": "1999-12-27T06:36:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum hall system",
      "spectral gaps",
      "pure infinite-volume ground state",
      "interaction",
      "non-zero excitation gap"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 54,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998cond.mat..9228K"
    }
  }
}