{
  "id": "1509.04649",
  "version": "v1",
  "published": "2015-09-15T17:18:53.000Z",
  "updated": "2015-09-15T17:18:53.000Z",
  "title": "Dynamics of decoherence: universal scaling of the decoherence factor",
  "authors": [
    "Sei Suzuki",
    "Tanay Nag",
    "Amit Dutta"
  ],
  "comment": "4 pages, 4 figures, 6 pages supplementary material",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the time dependence of the decoherence factor (DF) of a qubit globally coupled to an environmental spin system (ESS) which is driven across the quantum critical point (QCP) by varying a parameter of its Hamiltonian in time $t$ as $1 -t/\\tau$ or $-t/\\tau$, to which the qubit is coupled starting at the time $t \\to -\\infty$; here, $\\tau$ denotes the inverse quenching rate. In the limit of weak coupling, we analyze the time evolution of the DF in the vicinity of the QCP (chosen to be at $t=0$) and define three quantities, namely, the generalized fidelity susceptibility $\\chi_F(\\tau)$ (defined right at the QCP), and the decay constants $\\alpha_1 (\\tau)$ and $\\alpha_2 (\\tau)$ which dictate the decay of the DF at a small but finite $t$($>0$). Using a dimensional analysis argument based on the Kibble-Zurek healing length, we show that $\\chi_F(\\tau)$ as well as $\\alpha_1 (\\tau)$ and $\\alpha_2(\\tau)$ indeed satisfy universal power-law scaling relations with $\\tau$ and the exponents are solely determined by the spatial dimensionality of the ESS and the exponents associated with its QCP. Remarkably, using the numerical t-DMRG method, these scaling relations are shown to be valid in both the situations when the ESS is integrable and non-integrable and also for both linear and non-linear variation of the parameter. Furthermore, when an integrable ESS is quenched far away from the QCP, there is a predominant Gaussian decay of the DF with a decay constant which also satisfies a universal scaling relation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-15T17:18:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "decoherence factor",
      "universal scaling",
      "satisfy universal power-law scaling relations",
      "decay constant",
      "dimensional analysis argument"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}