{
  "id": "0807.0259",
  "version": "v2",
  "published": "2008-07-02T02:13:51.000Z",
  "updated": "2009-01-14T14:19:38.000Z",
  "title": "The Link between Integrability, Level Crossings, and Exact Solution in Quantum Models",
  "authors": [
    "H. K. Owusu",
    "K. Wagh",
    "E. A. Yuzbashyan"
  ],
  "comment": "33 pages, 10 figures, minor typos corrected, reference added, model generalized beyond real symmetric to Hermitian operators",
  "journal": "2009 J. Phys. A: Math. Theor. 42 035206",
  "doi": "10.1088/1751-8113/42/3/035206",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We investigate the connection between energy level crossings in integrable systems and their integrability, i.e. the existence of a set of non-trivial integrals of motion. In particular, we consider a general quantum Hamiltonian linear in the coupling u, H(u) = T + uV, and require that it has the maximum possible number of nontrivial commuting partners also linear in u. We demonstrate how this commutation requirement alone leads to: (1) an exact solution for the energy spectrum and (2) level crossings, which are always present in these Hamiltonians in violation of the Wigner-von Neumann non-crossing rule. Moreover, we construct these Hamiltonians explicitly by resolving the above commutation requirement and show their equivalence to a sector of Gaudin magnets (central spin Hamiltonians). In contrast, fewer than the maximum number of conservation laws does not guarantee level crossings.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-01-14T14:19:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exact solution",
      "quantum models",
      "integrability",
      "commutation requirement",
      "general quantum hamiltonian linear"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2009,
      "month": "Jan",
      "volume": 42,
      "number": 3,
      "pages": "035206"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009JPhA...42c5206O"
    }
  }
}