{
  "id": "1210.6613",
  "version": "v2",
  "published": "2012-10-24T17:37:17.000Z",
  "updated": "2014-11-24T16:21:18.000Z",
  "title": "Frustration free gapless Hamiltonians for Matrix Product States",
  "authors": [
    "Carlos Fernández-González",
    "Norbert Schuch",
    "Michael M. Wolf",
    "J. Ignacio Cirac",
    "David Pérez-García"
  ],
  "comment": "36 pages, new version with some contents rearranged, and a correction in the injective case",
  "doi": "10.1007/s00220-014-2173-z",
  "categories": [
    "quant-ph",
    "cond-mat.str-el"
  ],
  "abstract": "For every Matrix Product State (MPS) one can always construct a so-called parent Hamiltonian. This is a local, frustration free, Hamiltonian which has the MPS as ground state and is gapped. Whenever that parent Hamiltonian has a degenerate ground state (the so-called non-injective case), we construct another 'uncle' Hamiltonian which is local and frustration free but gapless, and its spectrum is $\\R^+$. The construction is obtained by linearly perturbing the matrices building up the state in a random direction, and then taking the limit where the perturbation goes to zero. For MPS where the parent Hamiltonian has a unique ground state (the so-called injective case) we also build such uncle Hamiltonian with the same properties in the thermodynamic limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-24T17:37:17.000Z",
      "comment": "34 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-24T16:21:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "matrix product state",
      "frustration free gapless hamiltonians",
      "parent hamiltonian",
      "degenerate ground state",
      "unique ground state"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Communications in Mathematical Physics",
      "year": 2015,
      "month": "Jan",
      "volume": 333,
      "number": 1,
      "pages": 299
    },
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015CMaPh.333..299F"
    }
  }
}