{
  "id": "2305.06336",
  "version": "v1",
  "published": "2023-05-10T17:44:33.000Z",
  "updated": "2023-05-10T17:44:33.000Z",
  "title": "Entanglement entropy and hyperuniformity of Ginibre and Weyl-Heisenberg ensembles",
  "authors": [
    "Luís Daniel Abreu"
  ],
  "categories": [
    "math-ph",
    "math.FA",
    "math.MP"
  ],
  "abstract": "We show that, for a class of planar determinantal point processes (DPP) X, the entanglement entropy of X on a compact region grows exactly at the rate of the variance fluctuation in that region. Therefore, such DPPs satisfy an area law if they are of Class I hyperuniformity, while the area law is violated if they are of Class II hyperuniformity. As a result, the entanglement entropy of Weyl-Heisenberg ensembles (a family of DPPs containing the Ginibre ensemble and Ginibre-type ensembles in higher Landau levels), satisfies an area law, as a consequence of its hyperuniformity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-10T17:44:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "entanglement entropy",
      "weyl-heisenberg ensembles",
      "hyperuniformity",
      "area law",
      "planar determinantal point processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}