{
  "id": "2009.14077",
  "version": "v1",
  "published": "2020-09-29T15:05:22.000Z",
  "updated": "2020-09-29T15:05:22.000Z",
  "title": "Sum rules for the supersymmetric eight-vertex model",
  "authors": [
    "Sandrine Brasseur",
    "Christian Hagendorf"
  ],
  "comment": "35 pages, no figures",
  "categories": [
    "math-ph",
    "math.MP",
    "nlin.SI"
  ],
  "abstract": "The eight-vertex model on the square lattice with vertex weights $a,b,c,d$ obeying the relation $(a^2+ab)(b^2+ab)=(c^2+ab)(d^2+ab)$ is considered. Its transfer matrix with $L=2n+1,\\, n\\geqslant 0,$ vertical lines and periodic boundary conditions along the horizontal direction has the doubly-degenerate eigenvalue $\\Theta_n = (a+b)^{2n+1}$. A basis of the corresponding eigenspace is investigated. Several scalar products involving the basis vectors are computed in terms of a family of polynomials introduced by Rosengren and Zinn-Justin. These scalar products are used to find explicit expressions for particular entries of the vectors. The proofs of these results are based on the generalisation of the eigenvalue problem for $\\Theta_n$ to the inhomogeneous eight-vertex model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-29T15:05:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "supersymmetric eight-vertex model",
      "sum rules",
      "scalar products",
      "periodic boundary conditions",
      "explicit expressions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}