{
  "id": "0802.3221",
  "version": "v2",
  "published": "2008-02-21T21:29:38.000Z",
  "updated": "2008-04-04T23:56:50.000Z",
  "title": "Entanglement and Density Matrix of a Block of Spins in AKLT Model",
  "authors": [
    "Ying Xu",
    "Hosho Katsura",
    "Takaaki Hirano",
    "Vladimir E. Korepin"
  ],
  "comment": "Revised version, typos corrected, references added, 31 pages",
  "journal": "Jour. Stat. Phys. vol 133, no. 2, 347-377 (2008)",
  "doi": "10.1007/s10955-008-9617-9",
  "categories": [
    "quant-ph",
    "cond-mat.stat-mech",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study a 1-dimensional AKLT spin chain, consisting of spins $S$ in the bulk and $S/2$ at both ends. The unique ground state of this AKLT model is described by the Valence-Bond-Solid (VBS) state. We investigate the density matrix of a contiguous block of bulk spins in this ground state. It is shown that the density matrix is a projector onto a subspace of dimension $(S+1)^{2}$. This subspace is described by non-zero eigenvalues and corresponding eigenvectors of the density matrix. We prove that for large block the von Neumann entropy coincides with Renyi entropy and is equal to $\\ln(S+1)^{2}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-04-04T23:56:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "density matrix",
      "aklt model",
      "von neumann entropy coincides",
      "entanglement",
      "unique ground state"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Physics",
      "year": 2008,
      "month": "Oct",
      "volume": 133,
      "number": 2,
      "pages": 347
    },
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008JSP...133..347X"
    }
  }
}