{
  "id": "1105.5264",
  "version": "v1",
  "published": "2011-05-26T12:42:04.000Z",
  "updated": "2011-05-26T12:42:04.000Z",
  "title": "Ferromagnetic Ordering of Energy Levels for $U_q(\\mathfrak{sl}_2)$ Symmetric Spin Chains",
  "authors": [
    "Bruno Nachtergaele",
    "Stephen Ng",
    "Shannon Starr"
  ],
  "comment": "23 pages",
  "journal": "Lett. Math. Phys. 100, 327--356 (2012)",
  "doi": "10.1007/s11005-011-0538-1",
  "categories": [
    "math-ph",
    "math.MP",
    "math.PR",
    "math.QA"
  ],
  "abstract": "We consider the class of quantum spin chains with arbitrary $U_q(\\mathfrak{sl}_2)$-invariant nearest neighbor interactions, sometimes called $\\textrm{SU}_q(2)$ for the quantum deformation of $\\textrm{SU}(2)$, for $q>0$. We derive sufficient conditions for the Hamiltonian to satisfy the property we call {\\em Ferromagnetic Ordering of Energy Levels}. This is the property that the ground state energy restricted to a fixed total spin subspace is a decreasing function of the total spin. Using the Perron-Frobenius theorem, we show sufficient conditions are positivity of all interactions in the dual canonical basis of Lusztig. We characterize the cone of positive interactions, showing that it is a simplicial cone consisting of all non-positive linear combinations of \"cascade operators,\" a special new basis of $U_q(\\mathfrak{sl}_2)$ intertwiners we define. We also state applications to interacting particle processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-05-26T12:42:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B10",
      "82D40",
      "81R50",
      "60K35"
    ],
    "keywords": [
      "symmetric spin chains",
      "energy levels",
      "ferromagnetic ordering",
      "invariant nearest neighbor interactions",
      "ground state energy"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Letters in Mathematical Physics",
      "year": 2012,
      "month": "Jun",
      "volume": 100,
      "number": 3,
      "pages": 327
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012LMaPh.100..327N"
    }
  }
}