{
  "id": "1403.6157",
  "version": "v3",
  "published": "2014-03-24T21:18:04.000Z",
  "updated": "2014-07-31T20:54:22.000Z",
  "title": "Shannon and Rényi mutual information in quantum critical spin chains",
  "authors": [
    "Jean-Marie Stéphan"
  ],
  "comment": "20 pages, 13 figures. v2: minor corrections, table added, expanded appendices. v3: published version",
  "journal": "Phys. Rev. B 90, 045424 (2014)",
  "doi": "10.1103/PhysRevB.90.045424",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.str-el",
    "quant-ph"
  ],
  "abstract": "We study the Shannon mutual information in one-dimensional critical spin chains, following a recent conjecture (Phys. Rev. Lett. 111, 017201 (2013)), as well as R\\'enyi generalizations of it. We combine conformal field theory arguments with numerical computations in lattice discretizations with central charge $c=1$ and $c=1/2$. For a periodic system of length $L$ cut into two parts of length $\\ell$ and $L-\\ell$, all our results agree with the general shape-dependence $I_n(\\ell,L)=(b_n/4)\\ln \\left(\\frac{L}{\\pi}\\sin \\frac{\\pi \\ell}{L}\\right)$, where $b_n$ is a universal coefficient. For the free boson CFT we show from general arguments that $b_n=c=1$. At $c=1/2$ we conjecture a result for $n>1$. We perform extensive numerical computations in Ising chains to confirm this, and also find $b_1\\simeq 0.4801629(2)$, a nontrivial number which we do not understand analytically. Open chains at $c=1/2$ and $n=1$ are even more intriguing, with a shape-dependent logarithmic divergence of the Shannon mutual information.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-07-31T20:54:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "75.10.Pq",
      "03.67.Mn",
      "11.25.Hf"
    ],
    "keywords": [
      "quantum critical spin chains",
      "rényi mutual information",
      "shannon mutual information",
      "conformal field theory arguments",
      "one-dimensional critical spin chains"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review B",
      "year": 2014,
      "month": "Jul",
      "volume": 90,
      "number": 4,
      "pages": "045424"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014PhRvB..90d5424S"
    }
  }
}