{
  "id": "2006.14151",
  "version": "v1",
  "published": "2020-06-25T03:19:27.000Z",
  "updated": "2020-06-25T03:19:27.000Z",
  "title": "Hall conductance and the statistics of flux insertions in gapped interacting lattice systems",
  "authors": [
    "Anton Kapustin",
    "Nikita Sopenko"
  ],
  "comment": "35 pages",
  "categories": [
    "math-ph",
    "cond-mat.mes-hall",
    "cond-mat.str-el",
    "math.MP"
  ],
  "abstract": "We study charge transport for zero-temperature infinite-volume gapped lattice systems in two dimensions with short-range interactions. We show that the Hall conductance is locally computable and is the same for all systems which are in the same gapped phase. We provide a rigorous versions of Laughlin's flux-insertion argument which shows that for short-range entangled systems the Hall conductance is an integer multiple of e^2/h. We show that the Hall conductance determines the statistics of flux insertions. For bosonic short-range entangled systems, this implies that the Hall conductance is an even multiple of e^2/h. Finally, we adapt a proof of quantization of the Thouless charge pump to the case of infinite-volume gapped lattice systems in one dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-25T03:19:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hall conductance",
      "gapped interacting lattice systems",
      "flux insertions",
      "statistics",
      "short-range entangled systems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}