{
"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"
}
}
}