{
  "id": "2104.03312",
  "version": "v1",
  "published": "2021-04-07T17:59:57.000Z",
  "updated": "2021-04-07T17:59:57.000Z",
  "title": "Partial thermalisation of a two-state system coupled to a finite quantum bath",
  "authors": [
    "Philip JD Crowley",
    "Anushya Chandran"
  ],
  "comment": "31 pages, 12 figures",
  "categories": [
    "quant-ph",
    "cond-mat.dis-nn",
    "cond-mat.mes-hall",
    "cond-mat.stat-mech"
  ],
  "abstract": "The eigenstate thermalisation hypothesis (ETH) is a statistical characterisation of eigen-energies, eigenstates and matrix elements of local operators in thermalising quantum systems. We develop an ETH-like ansatz of a partially thermalising system composed of a spin-1/2 coupled to a finite quantum bath. The spin-bath coupling is sufficiently weak that ETH does not apply, but sufficiently strong that perturbation theory fails. We calculate (i) the distribution of fidelity susceptibilities, which takes a broadly distributed form, (ii) the distribution of spin eigenstate entropies, which takes a bi-modal form, (iii) infinite time memory of spin observables, (iv) the distribution of matrix elements of local operators on the bath, which is non-Gaussian, and (v) the intermediate entropic enhancement of the bath, which interpolates smoothly between zero and the ETH value of $\\log 2$. The enhancement is a consequence of rare many-body resonances, and is asymptotically larger than the typical eigenstate entanglement entropy. We verify these results numerically and discuss their connections to the many-body localisation transition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-07T17:59:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite quantum bath",
      "partial thermalisation",
      "two-state system",
      "local operators",
      "matrix elements"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}