{
  "id": "1106.4171",
  "version": "v2",
  "published": "2011-06-21T11:15:03.000Z",
  "updated": "2012-07-02T13:15:57.000Z",
  "title": "Haag duality and the distal split property for cones in the toric code",
  "authors": [
    "Pieter Naaijkens"
  ],
  "comment": "15 pages, 2 figures, v2: extended introduction",
  "journal": "Lett. Math. Phys. 101 (2012), 341-354",
  "doi": "10.1007/s11005-012-0572-7",
  "categories": [
    "math-ph",
    "math.MP",
    "math.OA",
    "quant-ph"
  ],
  "abstract": "We prove that Haag duality holds for cones in the toric code model. That is, for a cone Lambda, the algebra R_Lambda of observables localized in Lambda and the algebra R_{Lambda^c} of observables localized in the complement Lambda^c generate each other's commutant as von Neumann algebras. Moreover, we show that the distal split property holds: if Lambda_1 \\subset Lambda_2 are two cones whose boundaries are well separated, there is a Type I factor N such that R_{Lambda_1} \\subset N \\subset R_{Lambda_2}. We demonstrate this by explicitly constructing N.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-07-02T13:15:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81R15",
      "46L60",
      "81T05",
      "82B20"
    ],
    "keywords": [
      "distal split property holds",
      "toric code model",
      "haag duality holds",
      "von neumann algebras",
      "cone lambda"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Letters in Mathematical Physics",
      "year": 2012,
      "month": "Sep",
      "volume": 101,
      "number": 3,
      "pages": 341
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012LMaPh.101..341N"
    }
  }
}