{
  "id": "0907.4672",
  "version": "v5",
  "published": "2009-07-27T15:57:03.000Z",
  "updated": "2010-02-25T09:02:38.000Z",
  "title": "An area law for the entropy of low-energy states",
  "authors": [
    "Lluis Masanes"
  ],
  "comment": "6 pages + appendix, 1 figure",
  "journal": "Phys.Rev.A80:052104,2009",
  "doi": "10.1103/PhysRevA.80.052104",
  "categories": [
    "quant-ph",
    "cond-mat.str-el",
    "hep-lat"
  ],
  "abstract": "It is often observed in the ground state of spatially-extended quantum systems with local interactions that the entropy of a large region is proportional to its surface area. In some cases, this area law is corrected with a logarithmic factor. This contrasts with the fact that in almost all states of the Hilbert space, the entropy of a region is proportional to its volume. This paper shows that low-energy states have (at most) an area law with the logarithmic correction, provided two conditions hold: (i) the state has sufficient decay of correlations, (ii) the number of eigenstates with vanishing energy-density is not exponential in the volume. These two conditions are satisfied by many relevant systems. The central idea of the argument is that energy fluctuations inside a region can be observed by measuring the exterior and a superficial shell of the region.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2010-02-25T09:02:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.65.-w"
    ],
    "keywords": [
      "area law",
      "low-energy states",
      "energy fluctuations inside",
      "spatially-extended quantum systems",
      "superficial shell"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review A",
      "year": 2009,
      "month": "Nov",
      "volume": 80,
      "number": 5,
      "pages": "052104"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 873013,
      "adsabs": "2009PhRvA..80e2104M"
    }
  }
}