{
  "id": "1902.08479",
  "version": "v1",
  "published": "2019-02-22T13:02:05.000Z",
  "updated": "2019-02-22T13:02:05.000Z",
  "title": "Non-Hermitian Topology of Exceptional Points",
  "authors": [
    "Kohei Kawabata",
    "Takumi Bessho",
    "Masatoshi Sato"
  ],
  "comment": "6+14 pages, 3+0 figures, 1+8 tables",
  "categories": [
    "cond-mat.mes-hall",
    "math-ph",
    "math.MP",
    "physics.optics",
    "quant-ph"
  ],
  "abstract": "We present a general theory on topology of exceptional points. On the basis of two distinct complex-energy gaps, a point-like or line-like vacant region in the complex-energy plane, we reveal that gapless points in non-Hermitian systems are categorized into two: the one around which only a point-like gap is open and the other around which both gaps are open. Whereas the latter has counterparts to conventional Hermitian systems, the former is unique to non-Hermitian systems, characterizing exceptional points. Based on this observation, we complete classification of topologically stable symmetry-protected exceptional points at generic momentum points for each type of complex-energy gaps. This theory clarifies that exceptional points possess multiple topological structures identified by a couple of independent topological charges. Moreover, our classification theory predicts unknown exceptional points; an exceptional point in three dimensions is constructed as an illustration.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-22T13:02:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-hermitian topology",
      "possess multiple topological structures",
      "points possess multiple topological",
      "stable symmetry-protected exceptional points",
      "classification theory predicts unknown exceptional"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}