{
  "id": "1403.4538",
  "version": "v1",
  "published": "2014-03-18T17:07:25.000Z",
  "updated": "2014-03-18T17:07:25.000Z",
  "title": "Cumulants of time-integrated observables of closed quantum systems and PT-symmetry, with an application to the quantum Ising chain",
  "authors": [
    "James M. Hickey",
    "Emanuele Levi",
    "Juan P. Garrahan"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "quant-ph"
  ],
  "abstract": "We study the connection between the cumulants of a time-integrated observable of a quantum system and the PT-symmetry properties of the non-Hermitian deformation of the Hamiltonian from which the generating function of these cumulants is obtained. This non-Hermitian Hamiltonian can display regimes of broken and of unbroken PT-symmetry, depending on the parameters of the problem and on the counting field that sets the strength of the non-Hermitian perturbation. This in turn determines the analytic structure of the long-time cumulant generating function (CGF) for the time-integrated observable. We consider in particular the case of the time-integrated (longitudinal) magnetisation in the one-dimensional Ising model in a transverse field. We show that its long-time CGF is singular on a curve in the magnetic field/counting field plane that delimits a regime where PT-symmetry is spontaneously broken (which includes the static ferromagnetic phase), from one where it is preserved (which includes the static paramagnetic phase). In the paramagnetic phase, conservation of PT -symmetry implies that all cumulants are sub-linear in time, a behaviour usually associated to the absence of decorrelation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-03-18T17:07:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11.30.Qc",
      "05.30.Rt",
      "05.70.Ln"
    ],
    "keywords": [
      "closed quantum systems",
      "quantum ising chain",
      "time-integrated observable",
      "pt-symmetry",
      "application"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevB.90.094301",
      "journal": "Physical Review B",
      "year": 2014,
      "month": "Sep",
      "volume": 90,
      "number": 9,
      "pages": "094301"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014PhRvB..90i4301H"
    }
  }
}