{
  "id": "quant-ph/0611264",
  "version": "v4",
  "published": "2006-11-28T19:31:34.000Z",
  "updated": "2007-07-04T09:23:19.000Z",
  "title": "Statistics dependence of the entanglement entropy",
  "authors": [
    "M. Cramer",
    "J. Eisert",
    "M. B. Plenio"
  ],
  "comment": "4 pages, 1 figure (essentially identical with published version)",
  "journal": "Phys.Rev.Lett.98:220603,2007",
  "doi": "10.1103/PhysRevLett.98.220603",
  "categories": [
    "quant-ph",
    "cond-mat.other",
    "hep-th"
  ],
  "abstract": "The entanglement entropy of a distinguished region of a quantum many-body system reflects the entanglement present in its pure ground state. In this work, we establish scaling laws for this entanglement for critical quasi-free fermionic and bosonic lattice systems, without resorting to numerical means. We consider the geometrical setting of D-dimensional half-spaces which allows us to exploit a connection to the one-dimensional case. Intriguingly, we find a difference in the scaling properties depending on whether the system is bosonic - where an area-law is first proven to hold - or fermionic, extending previous findings for cubic regions. For bosonic systems with nearest neighbor interaction we prove the conjectured area-law by computing the logarithmic negativity analytically. We identify a length scale associated with entanglement, different from the correlation length. For fermions we determine the logarithmic correction to the area-law, which depends on the topology of the Fermi surface. We find that Lifshitz quantum phase transitions are accompanied with a non-analyticity in the prefactor of the leading order term.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2007-07-04T09:23:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.50.+q",
      "05.70.-a",
      "03.67.Mn",
      "05.30.-d"
    ],
    "keywords": [
      "entanglement entropy",
      "statistics dependence",
      "lifshitz quantum phase transitions",
      "quantum many-body system reflects",
      "nearest neighbor interaction"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. Lett."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 736002
    }
  }
}