{
  "id": "cond-mat/0510604",
  "version": "v1",
  "published": "2005-10-23T18:24:42.000Z",
  "updated": "2005-10-23T18:24:42.000Z",
  "title": "Exact solution of Z_2 Chern-Simons model on a triangular lattice",
  "authors": [
    "B. Doucot",
    "L. B. Ioffe"
  ],
  "comment": "7 pages, 4 figures",
  "journal": "Phys. Rev. A 72, 032303 (2005)",
  "doi": "10.1103/PhysRevA.72.032303",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We construct the Hamiltonian description of the Chern-Simons theory with Z_n gauge group on a triangular lattice. We show that the Z_2 model can be mapped onto free Majorana fermions and compute the excitation spectrum. In the bulk the spectrum turns out to be gapless but acquires a gap if a magnetic term is added to the Hamiltonian. On a lattice edge one gets additional non-gauge invariant (matter) gapless degrees of freedom whose number grows linearly with the edge length. Therefore, a small hole in the lattice plays the role of a charged particle characterized by a non-trivial projective representation of the gauge group, while a long edge provides a decoherence mechanism for the fluxes. We discuss briefly the implications for the implementations of protected qubits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-10-23T18:24:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "triangular lattice",
      "chern-simons model",
      "exact solution",
      "gauge group",
      "free majorana fermions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. A"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}