{
  "id": "1811.04638",
  "version": "v1",
  "published": "2018-11-12T10:24:19.000Z",
  "updated": "2018-11-12T10:24:19.000Z",
  "title": "Quantum Geometric Tensor in $\\mathcal{PT}$-Symmetric Quantum Mechanics",
  "authors": [
    "Da-Jian Zhang",
    "Qing-hai Wang",
    "Jiangbin Gong"
  ],
  "comment": "main text of 5 pages, plus supplementary material of 8 pages",
  "categories": [
    "quant-ph"
  ],
  "abstract": "A series of geometric concepts are formulated for $\\mathcal{PT}$-symmetric quantum mechanics and they are further unified into one entity, i.e., an extended quantum geometric tensor (QGT). The imaginary part of the extended QGT gives a Berry curvature whereas the real part induces a metric tensor on system's parameter manifold. This results in a unified conceptual framework to understand and explore physical properties of $\\mathcal{PT}$-symmetric systems from a geometric perspective. To illustrate the usefulness of the extended QGT, we show how its real part, i.e., the metric tensor, can be exploited as a tool to detect quantum phase transitions as well as spontaneous $\\mathcal{PT}$-symmetry breaking in $\\mathcal{PT}$-symmetric systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-12T10:24:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric quantum mechanics",
      "symmetric systems",
      "detect quantum phase transitions",
      "extended qgt",
      "systems parameter manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}