{
  "id": "1811.09899",
  "version": "v1",
  "published": "2018-11-24T21:24:01.000Z",
  "updated": "2018-11-24T21:24:01.000Z",
  "title": "A Schrödinger Operator Approach to Higher Spin XXZ Systems on General Graphs",
  "authors": [
    "Christoph Fischbacher"
  ],
  "comment": "16 pages, Contribution to the Proceedings of the Arizona School of Analysis and Mathematical Physics 2018",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider the spin-$J$ XXZ-Hamiltonian on general graphs $\\mathcal{G}$ and show its equivalence to a direct sum of discrete many-particle Schr\\\"odinger type operators on what we call \"$N$-particle graphs with maximal local occupation number $M$\", where the kinetic term is described by a weighted Laplacian. Generalizing previous results for the spin-$1/2$ case, we give sufficient conditions for the existence of spectral gaps above the low-lying droplet band when the underlying graph $\\mathcal{G}$ is (i) the chain and (ii) a strip of width $L$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-24T21:24:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B20"
    ],
    "keywords": [
      "higher spin xxz systems",
      "schrödinger operator approach",
      "general graphs",
      "maximal local occupation number",
      "spectral gaps"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}