{
  "id": "2302.00465",
  "version": "v1",
  "published": "2023-02-01T14:25:39.000Z",
  "updated": "2023-02-01T14:25:39.000Z",
  "title": "The Spectral Gap and Low-Energy Spectrum in Mean-Field Quantum Spin Systems",
  "authors": [
    "Chokri Manai",
    "Simone Warzel"
  ],
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "math.MP"
  ],
  "abstract": "A semiclassical analysis based on spin-coherent states is used to establish a classification and formulae for the spectral gap of mean-field spin Hamiltonians. For gapped systems we provide a full description of the low-energy spectra based on a second-order approximation to the semiclassical Hamiltonian hence justifying fluctuation theory at zero temperature for this case. We also point out a shift caused by the spherical geometry in these second-order approximations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-01T14:25:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q10",
      "81R30"
    ],
    "keywords": [
      "mean-field quantum spin systems",
      "low-energy spectrum",
      "spectral gap",
      "second-order approximation",
      "mean-field spin hamiltonians"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}