{
  "id": "1403.3040",
  "version": "v1",
  "published": "2014-03-12T17:32:07.000Z",
  "updated": "2014-03-12T17:32:07.000Z",
  "title": "Thermalization and Revivals after a Quantum Quench in Conformal Field Theory",
  "authors": [
    "John Cardy"
  ],
  "comment": "5 pages, 3 figures",
  "journal": "Phys. Rev. Lett. 112, 220401 (2014)",
  "doi": "10.1103/PhysRevLett.112.220401",
  "categories": [
    "cond-mat.stat-mech",
    "hep-th"
  ],
  "abstract": "We consider a quantum quench in a finite system of length $L$ described by a 1+1-dimensional CFT, of central charge $c$, from a state with finite energy density corresponding to an inverse temperature $\\beta\\ll L$. For times $t$ such that $\\ell/2<t<(L-\\ell)/2$ the reduced density matrix of a subsystem of length $\\ell$ is exponentially close to a thermal density matrix. We compute exactly the overlap $\\cal F$ of the state at time $t$ with the initial state and show that in general it is exponentially suppressed at large $L/\\beta$. However, for minimal models with $c<1$ (more generally, rational CFTs), at times which are integer multiples of $L/2$ (for periodic boundary conditions, $L$ for open boundary conditions) there are (in general, partial) revivals at which $\\cal F$ is $O(1)$, leading to an eventual complete revival with ${\\cal F}=1$. There is also interesting structure at all rational values of $t/L$, related to properties of the CFT under modular transformations. At early times $t\\!\\ll\\!(L\\beta)^{1/2}$ there is a universal decay ${\\cal F}\\sim\\exp\\big(\\!-\\!(\\pi c/3)Lt^2/\\beta(\\beta^2+4t^2)\\big)$. The effect of an irrelevant non-integrable perturbation of the CFT is to progressively broaden each revival at $t=nL/2$ by an amount $O(n^{1/2})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-12T17:32:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.30.Rt",
      "04.70.Dy",
      "11.25.Hf"
    ],
    "keywords": [
      "conformal field theory",
      "quantum quench",
      "thermalization",
      "thermal density matrix",
      "finite energy density"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review Letters",
      "year": 2014,
      "month": "Jun",
      "volume": 112,
      "number": 22,
      "pages": 220401
    },
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1285509,
      "adsabs": "2014PhRvL.112v0401C"
    }
  }
}