{
  "id": "1711.04397",
  "version": "v1",
  "published": "2017-11-13T02:49:35.000Z",
  "updated": "2017-11-13T02:49:35.000Z",
  "title": "On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions",
  "authors": [
    "Christian Hagendorf",
    "Jean Liénardy"
  ],
  "comment": "20 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The square-lattice eight-vertex model with statistical weights $a,b,c,d$ obeying the relation $(a^2+ab)(b^2+ab) = (c^2+ab)(d^2+ab)$ and periodic boundary conditions is considered. It is shown that the transfer matrix of the model for $L=2n+1$ vertical lines and periodic boundary conditions along the horizontal direction possesses the doubly-degenerate eigenvalue $\\Theta_n = (a+b)^{2n+1}$. This proves a conjecture by Stroganov from 2001. The proof uses the supersymmetry of a related XYZ spin-chain Hamiltonian. The eigenstates of the transfer matrix corresponding to $\\Theta_n$ are shown to be the ground states of the spin-chain Hamiltonian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-13T02:49:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "periodic boundary conditions",
      "transfer matrix",
      "supersymmetric eight-vertex model",
      "square-lattice eight-vertex model",
      "related xyz spin-chain hamiltonian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}