{
  "id": "0911.4215",
  "version": "v3",
  "published": "2009-11-22T17:40:26.000Z",
  "updated": "2010-04-27T23:23:16.000Z",
  "title": "Derivation of Matrix Product Ansatz for the Heisenberg Chain from Algebraic Bethe Ansatz",
  "authors": [
    "Hosho Katsura",
    "Isao Maruyama"
  ],
  "comment": "24 pages; minor typos are corrected",
  "journal": "J. Phys. A: Math. Theor. 43 (2010) 175003",
  "doi": "10.1088/1751-8113/43/17/175003",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.str-el",
    "hep-th",
    "math-ph",
    "math.MP",
    "quant-ph"
  ],
  "abstract": "We derive a matrix product representation of the Bethe ansatz state for the XXX and XXZ spin-1/2 Heisenberg chains using the algebraic Bethe ansatz. In this representation, the components of the Bethe eigenstates are expressed as traces of products of matrices which act on ${\\bar {\\mathscr H}}$, the tensor product of auxiliary spaces. By changing the basis in ${\\bar {\\mathscr H}}$, we derive explicit finite-dimensional representations for the matrices. These matrices are the same as those appearing in the recently proposed matrix product ansatz by Alcaraz and Lazo [Alcaraz F C and Lazo M J 2006 {\\it J. Phys. A: Math. Gen.} \\textbf{39} 11335.] apart from normalization factors. We also discuss the close relation between the matrix product representation of the Bethe eigenstates and the six-vertex model with domain wall boundary conditions [Korepin V E 1982 {\\it Commun. Math. Phys.}, \\textbf{86} 391.] and show that the change of basis corresponds to a mapping from the six-vertex model to the five-vertex model.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-04-27T23:23:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "matrix product ansatz",
      "algebraic bethe ansatz",
      "heisenberg chain",
      "matrix product representation",
      "domain wall boundary conditions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2010,
      "month": "Apr",
      "volume": 43,
      "number": 17,
      "pages": 175003
    },
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 837624,
      "adsabs": "2010JPhA...43q5003K"
    }
  }
}