{
  "id": "2103.12501",
  "version": "v1",
  "published": "2021-03-23T12:58:00.000Z",
  "updated": "2021-03-23T12:58:00.000Z",
  "title": "Scalar product for the XXZ spin chain with general integrable boundaries",
  "authors": [
    "Samuel Belliard",
    "Rodrigo A. Pimenta",
    "Nikita A. Slavnov"
  ],
  "comment": "10 pages",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "hep-th",
    "math.MP"
  ],
  "abstract": "We calculate the scalar product of Bethe states of the XXZ spin-$\\frac{1}{2}$ chain with general integrable boundary conditions. The off-shell equations satisfied by the transfer matrix and the off-shell Bethe vectors allow one to derive a linear system for the scalar product of off-shell and on-shell Bethe states. We show that this linear system can be solved in terms of a compact determinant formula that involves the Jacobian of the transfer matrix eigenvalue and certain q-Pochhammer polynomials of the boundary couplings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-23T12:58:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "xxz spin chain",
      "scalar product",
      "linear system",
      "general integrable boundary conditions",
      "off-shell bethe vectors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}