{
  "id": "1105.4846",
  "version": "v3",
  "published": "2011-05-24T18:03:49.000Z",
  "updated": "2011-10-27T13:18:37.000Z",
  "title": "Local quantum quenches in critical one-dimensional systems: entanglement, the Loschmidt echo, and light-cone effects",
  "authors": [
    "Jean-Marie Stéphan",
    "Jérôme Dubail"
  ],
  "comment": "28 pages, 20 figures. v3: published version",
  "journal": "J. Stat. Mech. (2011) P08019",
  "doi": "10.1088/1742-5468/2011/08/P08019",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.str-el"
  ],
  "abstract": "We study a particular type of local quench in a generic quantum critical one-dimensional system, using conformal field theory (CFT) techniques, and providing numerical checks of the results in free fermion systems. The system is initially cut into two subsystems $A$ and $B$ which are glued together at time $t=0$. We study the entanglement entropy (EE) between the two parts $A$ and $B$, using previous results by Calabrese and Cardy, and further extending them. We also study in detail the (logarithmic) Loschmidt echo (LLE). For finite-size systems both quantities turn out to be (almost) periodic in the scaling limit, and exhibit striking light-cone effects. While these two quantities behave similarly immediately after the quench---namely as $c/3 \\log t$ for the EE and $c/4 \\log t$ for the LLE---, we observe some discrepancy once the excitations emitted by the quench bounce on the boundary and evolve within the same subsystem $A$ (or $B$). The decay of the EE is then non-universal, as noticed by Eisler and Peschel. On the contrary, we find that the evolution of the LLE is less sensitive than the EE to non-universal details of the model, and is still accurately described by our CFT prediction. To further probe these light-cone effects, we also introduce a variant of the Loschmidt echo specifically constructed to detect the excitations emitted just after the quench.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-10-27T13:18:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "loschmidt echo",
      "local quantum quenches",
      "light-cone effects",
      "entanglement",
      "generic quantum critical one-dimensional system"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Statistical Mechanics: Theory and Experiment",
      "year": 2011,
      "month": "Aug",
      "volume": 2011,
      "number": 8,
      "pages": 8019
    },
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011JSMTE..08..019S"
    }
  }
}