{
"id": "2005.10814",
"version": "v1",
"published": "2020-05-21T17:49:52.000Z",
"updated": "2020-05-21T17:49:52.000Z",
"title": "Information scrambling at finite temperature in local quantum systems",
"authors": [
"Subhayan Sahu",
"Brian Swingle"
],
"comment": "28+17 pages",
"categories": [
"cond-mat.stat-mech",
"cond-mat.str-el",
"hep-th",
"quant-ph"
],
"abstract": "This paper investigates the temperature dependence of quantum information scrambling in local systems with an energy gap, $m$, above the ground state. We study the speed and shape of growing Heisenberg operators as quantified by out-of-time-order correlators, with particular attention paid to so-called contour dependence, i.e. dependence on the way operators are distributed around the thermal circle. We report large scale tensor network numerics on a gapped chaotic spin chain down to temperatures comparable to the gap which show that the speed of operator growth is strongly contour dependent. The numerics also show a characteristic broadening of the operator wavefront at finite temperature $T$. To study the behavior at temperatures much below the gap, we perform a perturbative calculation in the paramagnetic phase of a 2+1D O($N$) non-linear sigma model, which is analytically tractable at large $N$. Using the ladder diagram technique, we find that operators spread at a speed $\\sqrt{T/m}$ at low temperatures, $T\\ll m$. In contrast to the numerical findings of spin chain, the large $N$ computation is insensitive to the contour dependence and does not show broadening of operator front. We discuss these results in the context of a recently proposed state-dependent bound on scrambling.",
"revisions": [
{
"version": "v1",
"updated": "2020-05-21T17:49:52.000Z"
}
],
"analyses": {
"keywords": [
"local quantum systems",
"finite temperature",
"information scrambling",
"large scale tensor network numerics",
"report large scale tensor network"
],
"note": {
"typesetting": "TeX",
"pages": 17,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}