{
  "id": "0910.3003",
  "version": "v2",
  "published": "2009-10-15T21:41:59.000Z",
  "updated": "2009-10-26T16:37:07.000Z",
  "title": "Entanglement entropy and the complex plane of replicas",
  "authors": [
    "F. Gliozzi",
    "L. Tagliacozzo"
  ],
  "comment": "24 pages, 9 figures. v2: typos corrected, two figures replaced",
  "journal": "J. Stat. Mech. (2010) P01002",
  "doi": "10.1088/1742-5468/2010/01/P01002",
  "categories": [
    "cond-mat.stat-mech",
    "hep-th",
    "quant-ph"
  ],
  "abstract": "The entanglement entropy of a subsystem $A$ of a quantum system is expressed, in the replica method, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix $\\tr\\rho_A^n$. We study the analytic properties of this quantity as a function of n in some quantum critical Ising-like models in 1+1 and 2+1 dimensions. Although we find no true singularities for n>0, there is a threshold value of n close to 2 which separates two very different `phases'. The region with larger n is characterized by rapidly convergent Taylor expansions and is very smooth. The region with smaller n has a very rich and varied structure in the complex n plane and is characterized by Taylor coefficients which instead of being monotone decreasing, have a maximum growing with the size of the subsystem. Finite truncations of the Taylor expansion in this region lead to increasingly poor approximations of $\\tr\\rho_A^n$. The computation of the entanglement entropy from the knowledge of $\\tr\\rho^n_A$ for positive integer n becomes extremely difficult particularly in spatial dimensions larger than one, where one cannot use conformal field theory as a guidance in the extrapolations to n=1.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-10-26T16:37:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "entanglement entropy",
      "complex plane",
      "conformal field theory",
      "rapidly convergent taylor expansions",
      "spatial dimensions larger"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Mechanics: Theory and Experiment",
      "year": 2010,
      "month": "Jan",
      "volume": 2010,
      "number": 1,
      "pages": 1002
    },
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 849819,
      "adsabs": "2010JSMTE..01..002G"
    }
  }
}