{
  "id": "1301.1930",
  "version": "v4",
  "published": "2013-01-09T17:18:31.000Z",
  "updated": "2013-04-08T15:48:02.000Z",
  "title": "Role of marginality in quantum fidelity and Loschmidt echo: Dirac points in 2-D",
  "authors": [
    "Aavishkar A. Patel",
    "Shraddha Sharma",
    "Amit Dutta"
  ],
  "comment": "6 pages, 3 figures",
  "journal": "EPL, 102 (2013) 46001",
  "doi": "10.1209/0295-5075/102/46001",
  "categories": [
    "cond-mat.mes-hall",
    "quant-ph"
  ],
  "abstract": "We investigate the effect of marginality on the ground state fidelity and Loschmidt echo. For this purpose, we study the above quantities near the quantum critical point (QCP) of the two-dimensional (2-D) Dirac Hamiltonian in the presence of a mass term which is tuned to zero at the Dirac point. An ideal example would be that of the low-energy carriers in graphene in which a mass term opens up a band gap. This happens to be a marginal situation where the behavior of the fidelity and the echo is markedly different as compared to that in the one-dimensional case. We encounter this marginal behavior near the Dirac point, which is displayed in the absence of a sharp dip in the ground state fidelity (or equivalently in the logarithmic scaling of the fidelity susceptibility). Most importantly, there is also a logarithmic correction to the proposed scaling of the fidelity in the thermodynamic limit which can not be a priori anticipated from the predicted scaling form. Interestingly, a sharp dip in the ground state Loschmidt echo is also found to be absent near this QCP, which is again a consequence of the marginality. We also explain the absence of a sharp dip in both the fidelity and the Loschmidt echo close to the QCP in dimensions greater than two.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-04-08T15:48:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirac point",
      "quantum fidelity",
      "ground state fidelity",
      "sharp dip",
      "marginality"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "EPL (Europhysics Letters)",
      "year": 2013,
      "month": "May",
      "volume": 102,
      "number": 4,
      "pages": 46001
    },
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013EL....10246001P"
    }
  }
}