{
  "id": "1103.3247",
  "version": "v2",
  "published": "2011-03-16T18:16:58.000Z",
  "updated": "2012-08-03T16:24:16.000Z",
  "title": "Entanglement entropy of highly degenerate states and fractal dimensions",
  "authors": [
    "Olalla A. Castro-Alvaredo",
    "Benjamin Doyon"
  ],
  "comment": "5 pages. v2: Small changes, published version",
  "journal": "Phys. Rev. Lett. 108, 120401 (2012)",
  "doi": "10.1103/PhysRevLett.108.120401",
  "categories": [
    "cond-mat.stat-mech",
    "hep-th"
  ],
  "abstract": "We consider the bipartite entanglement entropy of ground states of extended quantum systems with a large degeneracy. Often, as when there is a spontaneously broken global Lie group symmetry, basis elements of the lowest-energy space form a natural geometrical structure. For instance, the spins of a spin-1/2 representation, pointing in various directions, form a sphere. We show that for subsystems with a large number m of local degrees of freedom, the entanglement entropy diverges as (d/2) log m, where d is the fractal dimension of the subset of basis elements with nonzero coefficients. We interpret this result by seeing d as the (not necessarily integer) number of zero-energy Goldstone bosons describing the ground state. We suggest that this result holds quite generally for largely degenerate ground states, with potential applications to spin glasses and quenched disorder.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-08-03T16:24:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.Ud",
      "75.10.Pq",
      "65.40.gd",
      "11.25.Hf"
    ],
    "keywords": [
      "entanglement entropy",
      "highly degenerate states",
      "fractal dimension",
      "ground state",
      "broken global lie group symmetry"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review Letters",
      "year": 2012,
      "month": "Mar",
      "volume": 108,
      "number": 12,
      "pages": 120401
    },
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 892784,
      "adsabs": "2012PhRvL.108l0401C"
    }
  }
}