{
  "id": "2104.11581",
  "version": "v1",
  "published": "2021-04-23T13:30:05.000Z",
  "updated": "2021-04-23T13:30:05.000Z",
  "title": "Entanglement of Free Fermions on Johnson Graphs",
  "authors": [
    "Pierre-Antoine Bernard",
    "Nicolas Crampe",
    "Luc Vinet"
  ],
  "comment": "24 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Free fermions on Johnson graphs $J(n,k)$ are considered and the entanglement entropy of sets of neighborhoods is computed. For a subsystem composed of a single neighborhood, an analytical expression is provided by the decomposition in irreducible submodules of the Terwilliger algebra of $J(n,k)$ embedded in two copies of $\\mathfrak{su}(2)$. For a subsytem composed of multiple neighborhoods, the construction of a block-tridiagonal operator which commutes with the entanglement Hamiltonian is presented, its usefulness in computing the entropy is stressed and the area law pre-factor is discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-23T13:30:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free fermions",
      "johnson graphs",
      "area law pre-factor",
      "terwilliger algebra",
      "single neighborhood"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}