{
  "id": "2112.15567",
  "version": "v2",
  "published": "2021-12-31T17:42:34.000Z",
  "updated": "2022-02-07T16:54:53.000Z",
  "title": "Proxy ensemble geometric phase and proxy index of time-reversal invariant topological insulators at finite temperatures",
  "authors": [
    "Aixin Pi",
    "Ye Zhang",
    "Yan He",
    "Chih-Chun Chien"
  ],
  "comment": "11 pages, 7 figures, submitted",
  "categories": [
    "cond-mat.mes-hall",
    "quant-ph"
  ],
  "abstract": "The ensemble geometric phase (EGP) has been proposed as a topological indicator for finite-temperatures systems. The ensemble Wilson loop, or the transfer matrix, contains the crucial information in the EGP construction. We propose a proxy index and a proxy EGP directly from the transfer matrix and apply them to time-reversal invariant topological insulators exemplified by the Bernevig-Hughes-Zhang (BHZ) and Kane-Mele (KM) models. The quantized proxy index and proxy EGP smoothly generalize the ground-state topological index to finite temperatures. For the BHZ model, a comparison with another topological indicator, the Uhlmann phase, shows different transition behavior with temperature. For the KM model, the EGP have been generalized to the time-reversal EGP previously, but the proxy EGP does not require any splitting of the contributions. The proxy index and proxy EGP thus offer an efficient means for characterizing finite-temperature topological properties.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-02-07T16:54:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "time-reversal invariant topological insulators",
      "proxy ensemble geometric phase",
      "proxy index",
      "finite temperatures",
      "proxy egp"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}