{
  "id": "2309.16462",
  "version": "v1",
  "published": "2023-09-28T14:20:21.000Z",
  "updated": "2023-09-28T14:20:21.000Z",
  "title": "Spin Drude weight for the integrable XXZ chain with arbitrary spin",
  "authors": [
    "Shinya Ae",
    "Kazumitsu Sakai"
  ],
  "comment": "37 pages",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Using generalized hydrodynamics (GHD), we exactly evaluate the finite-temperature spin Drude weight in a zero magnetic field for the integrable XXZ chain with arbitrary spin and easy-plane anisotropy. First, we construct the fusion hierarchy of the quantum transfer matrices ($T$-functions) and derive functional relations ($T$- and $Y$-systems) satisfied by the $T$-functions and certain combinations of them ($Y$-functions). Through analytical arguments, the $Y$-system is reduced to a set of non-linear integral equations, equivalent to the thermodynamic Bethe ansatz (TBA) equations. Then, employing GHD, we calculate the spin Drude weight at arbitrary finite temperatures. As a result, a characteristic fractal-like structure of the Drude weight is observed at arbitrary spin, similar to the spin-1/2 case. In our approach, the solutions to the TBA equations (i.e., the $Y$-functions) can be explicitly written in terms of the $T$-functions, thus allowing for a systematic calculation of the high-temperature limit of the Drude weight.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-28T14:20:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "integrable xxz chain",
      "arbitrary spin",
      "finite-temperature spin drude weight",
      "quantum transfer matrices",
      "arbitrary finite temperatures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}