{
  "id": "1606.06631",
  "version": "v1",
  "published": "2016-06-21T15:56:04.000Z",
  "updated": "2016-06-21T15:56:04.000Z",
  "title": "Classification of excited-state quantum phase transitions for arbitrary number of degrees of freedom",
  "authors": [
    "Pavel Stránský",
    "Pavel Cejnar"
  ],
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Classical stationary points of an analytic Hamiltonian induce singularities of the density of quantum energy levels and their flow with a control parameter in the system's infinite-size limit. We show that for a system with $f$ degrees of freedom, a non-degenerate stationary point with index $r$ causes a discontinuity (for $r$ even) or divergence ($r$ odd) of the $(f-1)$ th derivative of both density and flow of the spectrum. An increase of flatness for a degenerate stationary point shifts the singularity to lower derivatives. The findings are verified in an $f=3$ toy model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-21T15:56:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "excited-state quantum phase transitions",
      "arbitrary number",
      "classification",
      "analytic hamiltonian induce singularities",
      "degenerate stationary point shifts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}