{
  "id": "1403.0163",
  "version": "v1",
  "published": "2014-03-02T05:44:04.000Z",
  "updated": "2014-03-02T05:44:04.000Z",
  "title": "Exact Mapping from Singular Value Spectrum of Fractal Images to Entanglement Spectrum of One-Dimensional Quantum Systems",
  "authors": [
    "Ching Hua Lee",
    "Yuki Yamada",
    "Tatsuya Kumamoto",
    "Hiroaki Matsueda"
  ],
  "comment": "5 pages, 3 figures",
  "categories": [
    "cond-mat.stat-mech",
    "hep-th"
  ],
  "abstract": "We examine the snapshot entropy of general fractal images defined by their singular values. Remarkably, the singular values for a large class of fractals are in exact correspondence with the entanglement spectrum of free fermions in one dimension. These fermions allow for a holographic interpretation of the logarithmic scaling of the snapshot entropy, which is in agreement with the Calabrese-Cardy formula. However, the coarse-grained entropy exhibits a linear scaling due to the degeneracy of the spectrum, in contrast with the logarithmic scaling behavior in one-dimensional quantum near-critical systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-02T05:44:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "one-dimensional quantum systems",
      "singular value spectrum",
      "entanglement spectrum",
      "exact mapping",
      "snapshot entropy"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.7566/JPSJ.84.013001",
      "journal": "Journal of the Physical Society of Japan",
      "year": 2015,
      "month": "Jan",
      "volume": 84,
      "number": 1,
      "pages": "013001"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1283360,
      "adsabs": "2015JPSJ...84a3001L"
    }
  }
}