{
  "id": "1803.01650",
  "version": "v1",
  "published": "2018-03-05T13:21:22.000Z",
  "updated": "2018-03-05T13:21:22.000Z",
  "title": "Off-Diagonal Observable Elements from Random Matrix Theory: Distributions, Fluctuations, and Eigenstate Thermalization",
  "authors": [
    "Charlie Nation",
    "Diego Porras"
  ],
  "comment": "17 + 7 Pages, 9 + 2 Figures",
  "categories": [
    "cond-mat.stat-mech",
    "quant-ph"
  ],
  "abstract": "We derive the Eigenstate Thermalization Hypothesis (ETH) from a random matrix Hamiltonian by extending the model introduced by J. M. Deutsch [Phys. Rev. A 43, 2046 (1991)]. We approximate the coupling between a subsystem and a many-body environment by means of a random Gaussian matrix. We show that a common assumption in the analysis of quantum chaotic systems, namely the treatment of eigenstates as independent random vectors, leads to inconsistent results. However, a consistent approach to the ETH can be developed by introducing an interaction between random wave-vectors that arises as a result of the orthonormality condition. This approach leads to a consistent form for off-diagonal matrix elements of observables. From there we obtain the scaling of time-averaged fluctuations with system size for which we calculate an analytic form in terms of the Inverse Participation Ratio. The analytic results are compared to exact diagonalizations of a quantum spin chain for different physical observables in multiple parameter regimes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-05T13:21:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random matrix theory",
      "off-diagonal observable elements",
      "fluctuations",
      "distributions",
      "random matrix hamiltonian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}