{
  "id": "2208.04014",
  "version": "v1",
  "published": "2022-08-08T09:52:37.000Z",
  "updated": "2022-08-08T09:52:37.000Z",
  "title": "Thermodynamics and criticality of su($m$) spin chains of Haldane-Shastry type",
  "authors": [
    "Federico Finkel",
    "Artemio González-López"
  ],
  "comment": "12 pages, 2 figures",
  "categories": [
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "We study the thermodynamics and critical behavior of su($m$) spin chains of Haldane-Shastry type at zero chemical potential, both in the $A_{N-1}$ and $BC_N$ cases. We evaluate in closed form the free energy per spin for arbitrary values of $m$, from which we derive explicit formulas for the energy, entropy and specific heat per spin. In particular, we find that the specific heat features a single Schottky peak, whose temperature is well approximated for $m\\lesssim10$ by the corresponding temperature for an $m$-level system with uniformly spaced levels. We show that at low temperatures the free energy per spin of the models under study behaves as that of a one-dimensional conformal field theory with central charge $c=m-1$ (with the only exception of the Frahm-Inozemtsev chain with zero value of its parameter). However, from a detailed study of the ground state degeneracy and the low-energy excitations, we conclude that these models are only critical in the antiferromagnetic case, with a few exceptions that we fully specify.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-08T09:52:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spin chains",
      "haldane-shastry type",
      "thermodynamics",
      "free energy",
      "criticality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}