{
  "id": "1403.6651",
  "version": "v2",
  "published": "2014-03-26T12:27:22.000Z",
  "updated": "2023-12-22T12:22:04.000Z",
  "title": "On correlation functions in the coordinate and the algebraic Bethe ansatz",
  "authors": [
    "Rafael Hernandez",
    "Juan Miguel Nieto"
  ],
  "comment": "41 pages. Latex. v2: Published version. Updated title and abstract",
  "journal": "Int. J. Theor. Phys. 62 (2023) no.12, 264",
  "doi": "10.1007/s10773-023-05519-1",
  "categories": [
    "hep-th"
  ],
  "abstract": "The Bethe ansatz, both in its coordinate and its algebraic version, is an exceptional method to compute the eigenvectors and eigenvalues of integrable systems. However, computing correlation functions using the eigenvectors thus constructed complicates rather fast. In this article, we will compute some simple correlation functions for the isotropic Heisenberg spin chain to highlight the shortcomings of both Bethe ans\\\"atze. In order to compare the results obtained from each approach, a discussion on the normalization of states in each ansatz will be required. We will show that the analysis can be extended to the long-range spin chain governing the spectrum of anomalous dimensions of single trace operators in four-dimensional Yang-Mills with maximal supersymmetry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-26T12:27:22.000Z",
      "title": "Correlation functions and the algebraic Bethe ansatz in the AdS/CFT correspondence",
      "abstract": "Inverse scattering and the algebraic Bethe ansatz can be used to reduce the evaluation of form factors and correlation functions to the calculation of a product of Bethe states. In this article we develop a method to compute correlation functions of spin operators located at arbitrary sites of the spin chain. We will focus our analysis on the SU(2) sector of N=4 supersymmetric Yang-Mills at weak-coupling. At one-loop we provide a systematic treatment of the apparent divergences arising from the algebra of the elements of the monodromy matrix of an homogeneous spin chain. Beyond one-loop the analysis can be extended through the map of the long-range Bethe ansatz to an inhomogeneous spin chain. We also show that a careful normalization of states in the spin chain requires choosing them as Zamolodchikov-Faddeev states.",
      "comment": "41 pages. Latex",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2023-12-22T12:22:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "algebraic bethe ansatz",
      "correlation functions",
      "spin chain",
      "ads/cft correspondence",
      "long-range bethe ansatz"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1287378,
      "adsabs": "2014arXiv1403.6651H"
    }
  }
}