{
  "id": "2012.06361",
  "version": "v1",
  "published": "2020-12-11T14:02:22.000Z",
  "updated": "2020-12-11T14:02:22.000Z",
  "title": "Eigenstate thermalization scaling in approaching the classical limit",
  "authors": [
    "Goran Nakerst",
    "Masudul Haque"
  ],
  "comment": "17 pages, 9 figures",
  "doi": "10.1103/PhysRevE.103.042109",
  "categories": [
    "cond-mat.stat-mech",
    "quant-ph"
  ],
  "abstract": "According to the eigenstate thermalization hypothesis (ETH), the eigenstate-to-eigenstate fluctuations of expectation values of local observables should decrease with increasing system size. In approaching the thermodynamic limit - the number of sites and the particle number increasing at the same rate - the fluctuations should scale as $\\sim D^{-1/2}$ with the Hilbert space dimension $D$. Here, we study a different limit - the classical or semiclassical limit - by increasing the particle number in fixed lattice topologies. We focus on the paradigmatic Bose-Hubbard system, which is quantum-chaotic for large lattices and shows mixed behavior for small lattices. We derive expressions for the expected scaling, assuming ideal eigenstates having Gaussian-distributed random components. We show numerically that, for larger lattices, ETH scaling of physical mid-spectrum eigenstates follows the ideal (Gaussian) expectation, but for smaller lattices, the scaling occurs via a different exponent. We examine several plausible mechanisms for this anomalous scaling.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-11T14:02:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "eigenstate thermalization scaling",
      "classical limit",
      "particle number",
      "eigenstate thermalization hypothesis",
      "hilbert space dimension"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}