{
  "id": "2403.03340",
  "version": "v1",
  "published": "2024-03-05T21:57:41.000Z",
  "updated": "2024-03-05T21:57:41.000Z",
  "title": "Relating the Hall conductivity to the many-body Chern number using Fermi's Golden rule and Kramers-Kronig relations",
  "authors": [
    "Nathan Goldman",
    "Tomoki Ozawa"
  ],
  "comment": "8 pages, 2 figures + Appendix",
  "categories": [
    "cond-mat.mes-hall",
    "cond-mat.quant-gas",
    "cond-mat.str-el",
    "quant-ph"
  ],
  "abstract": "This pedagogical piece provides a surprisingly simple demonstration that the quantized Hall conductivity of correlated insulators is given by the many-body Chern number, a topological invariant defined in the space of twisted boundary conditions. In contrast to conventional proofs, generally based on the Kubo formula, our approach entirely relies on combining Kramers-Kronig relations and Fermi's golden rule within a circular-dichroism framework. This pedagogical derivation illustrates how the Hall conductivity of correlated insulators can be determined by monitoring single-particle excitations upon a circular drive, a conceptually simple picture with direct implications for quantum-engineered systems, where excitation rates can be directly monitored.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-05T21:57:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fermis golden rule",
      "many-body chern number",
      "kramers-kronig relations",
      "correlated insulators",
      "quantized hall conductivity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}