{
  "id": "2201.10209",
  "version": "v1",
  "published": "2022-01-25T10:04:55.000Z",
  "updated": "2022-01-25T10:04:55.000Z",
  "title": "Heisenberg models and Schur--Weyl duality",
  "authors": [
    "Jakob Björnberg",
    "Hjalmar Rosengren",
    "Kieran Ryan"
  ],
  "comment": "55 pages, 9 figures",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We present a detailed analysis of certain quantum spin systems with inhomogeneous (non-random) mean-field interactions. Examples include, but are not limited to, the interchange- and spin singlet projection interactions on complete bipartite graphs. Using two instances of the representation theoretic framework of Schur--Weyl duality, we can explicitly compute the free energy and other thermodynamic limits in the models we consider. This allows us to describe the phase-transition, the ground-state phase diagram, and the expected structure of extremal states.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-01-25T10:04:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B26"
    ],
    "keywords": [
      "schur-weyl duality",
      "heisenberg models",
      "spin singlet projection interactions",
      "representation theoretic framework",
      "complete bipartite graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 55,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}