{
  "id": "2401.07449",
  "version": "v1",
  "published": "2024-01-15T03:27:19.000Z",
  "updated": "2024-01-15T03:27:19.000Z",
  "title": "Fock space: A bridge between Fredholm index and the quantum Hall effect",
  "authors": [
    "Guo Chuan Thiang",
    "Jingbo Xia"
  ],
  "categories": [
    "math-ph",
    "cond-mat.mes-hall",
    "math.FA",
    "math.MP",
    "math.QA"
  ],
  "abstract": "We identify the quantized Hall conductance of Landau levels with a Fredholm index, by using the theories of Helton-Howe-Carey-Pincus, and Toeplitz operators on the classic Fock space and higher Fock spaces. The index computations reduce to the single elementary one for the lowest Landau level. This brings new insights to the extraordinarily accurate quantization of the Hall conductance as measured in quantum Hall experiments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-15T03:27:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum hall effect",
      "fredholm index",
      "hall conductance",
      "classic fock space",
      "higher fock spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}