{
  "id": "1906.07736",
  "version": "v1",
  "published": "2019-06-18T18:00:05.000Z",
  "updated": "2019-06-18T18:00:05.000Z",
  "title": "Spectral statistics and many-body quantum chaos with conserved charge",
  "authors": [
    "Aaron J. Friedman",
    "Amos Chan",
    "Andrea De Luca",
    "J. T. Chalker"
  ],
  "comment": "4 pages main text + 10 pages supplementary material",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn",
    "cond-mat.str-el",
    "hep-th",
    "quant-ph"
  ],
  "abstract": "We investigate spectral statistics in spatially extended, chaotic many-body quantum systems with a conserved charge. We compute the spectral form factor $K(t)$ analytically for a minimal Floquet circuit model that has a $U(1)$ symmetry encoded via auxiliary spin-$1/2$ degrees of freedom. Averaging over an ensemble of realizations, we relate $K(t)$ to a partition function for the spins, given by a Trotterization of the spin-$1/2$ Heisenberg ferromagnet. Using Bethe Ansatz techniques, we extract the 'Thouless time' $t^{\\vphantom{*}}_{\\rm Th}$ demarcating the extent of random matrix behavior, and find scaling behavior governed by diffusion for $K(t)$ at $t\\lesssim t^{\\vphantom{*}}_{\\rm Th}$. We also report numerical results for $K(t)$ in a generic Floquet spin model, which are consistent with these analytic predictions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-18T18:00:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "many-body quantum chaos",
      "spectral statistics",
      "conserved charge",
      "chaotic many-body quantum systems",
      "generic floquet spin model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}