{
  "id": "1407.5294",
  "version": "v2",
  "published": "2014-07-20T14:16:16.000Z",
  "updated": "2014-10-14T12:47:44.000Z",
  "title": "Retrieve the Bethe states of quantum integrable models solved via off-diagonal Bethe Ansatz",
  "authors": [
    "Junpeng Cao",
    "Wen-Li Yang",
    "Kangjie Shi",
    "Yupeng Wang"
  ],
  "comment": "28 pages, no figure, extensively revised version with new contents about the open XXX spin chain. Two new authors are added",
  "categories": [
    "math-ph",
    "cond-mat.stat-mech",
    "hep-th",
    "math.MP"
  ],
  "abstract": "Based on the inhomogeneous T-Q relation constructed via the off-diagonal Bethe Ansatz (ODBA), a systematic method for retrieving the Bethe-type eigenstates of integrable models is developed by employing certain orthogonal basis of the Hilbert space. With the XXZ spin torus model and the open XXX spin-1/2 chain as examples, we show that for a given inhomogeneous T-Q relation and the associated Bethe Ansatz equations (BAEs), a corresponding Bethe-type eigenstate of the transfer matrix can be constructed. This scheme allows us to reach the homogeneous limit of the separation of variables (SoV) eigenstates and therefore provides a clear connection among the ODBA, the SoV and the algebraic Bethe Ansatz.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-20T14:16:16.000Z",
      "title": "Retrieve the Bethe states of quantum integrable models solved via off-diagonal Bethe ansatz",
      "abstract": "Based on the inhomogeneous T-Q relation constructed via the off-diagonal Bethe ansatz (ODBA), a systematic method for retrieving the Bethe-type eigenstates of integrable models is developed by employing an orthogonal basis of the Hilbert space. With the XXZ spin torus model as an example, we show that for a given inhomogeneous T-Q relation and the associated Bethe ansatz equations (BAEs), a corresponding Bethe-type eigenstate of the transfer matrix exists. It is found that in contrast to the usual ones, the derived reference state is no longer a pure state but a highly entangled many-body state. The corresponding off-shell scalar products are also obtained in the same framework.",
      "comment": "17 pages, no figure",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-10-14T12:47:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "off-diagonal bethe ansatz",
      "quantum integrable models",
      "bethe states",
      "inhomogeneous t-q relation",
      "bethe-type eigenstate"
    ],
    "publication": {
      "doi": "10.1088/1742-5468/2015/05/P05014",
      "journal": "Journal of Statistical Mechanics: Theory and Experiment",
      "year": 2015,
      "month": "May",
      "volume": 2015,
      "number": 5,
      "pages": "05014"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1307124,
      "adsabs": "2015JSMTE..05..014Z"
    }
  }
}