{
  "id": "1908.02596",
  "version": "v1",
  "published": "2019-08-07T12:44:14.000Z",
  "updated": "2019-08-07T12:44:14.000Z",
  "title": "Out of equilibrium mean field dynamics in the transverse field Ising model",
  "authors": [
    "Ingo Homrighausen",
    "Stefan Kehrein"
  ],
  "comment": "24 pages",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.str-el"
  ],
  "abstract": "Mean field type approximations are one of the most accessible methods to study the complexity of quantum many body systems out of equilibrium. However, the validity of such approximations has to be examined in each case. In this paper we investigate the transverse field Ising model on a finite fully connected lattice as one of the prime examples of mean field models. The mean field approximation becomes exact in the thermodynamic limit. We study the non-equilibrium dynamics after a sudden quantum quench. By exploiting the fully connected geometry and semi-classical intuition, we systematically expand around the mean field limit, and compute the leading order corrections analytically. We observe that dephasing effects can quickly, on a timescale given by the square root of the system size, lead to deviations from the mean field approximation in out of equilibrium situations, even for large systems and away from unstable fixed points where mean field is expected to be valid. The focus is twofold. First, we investigate the dynamics of the order parameter and its variance. Second, we investigate the entanglement with respect to a bipartition of the lattice. An analytic expression for the leading contribution of the family of Renyi entanglement entropies is given and a close connection to spin squeezing is confirmed quantitatively. The discussion of the dynamical phase diagram based on the order parameter and its variance translates directly to a discussion of the order parameter independent entanglement entropy. In particular, entanglement entropy grows logarithmically in time for quenches in the regime of periodically enhanced squeezing. Even though the paper focuses on the specific model of the transverse field Ising model, the findings are universal and translate to other models that permit a semi-classical effective description.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-07T12:44:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "transverse field ising model",
      "equilibrium mean field dynamics",
      "parameter independent entanglement entropy",
      "mean field approximation",
      "order parameter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}