



01894nas a2200193   4500008004100000245005300041210005200094260001400146520125500160653006101415653002701476653003501503653003101538100002901569700002001598700002001618700002501638856003701663       2022                        eng d00aDisordered Lieb-Robinson bounds in one dimension0 aDisordered LiebRobinson bounds in one dimension  c8/10/20223 a<p>By tightening the conventional Lieb-Robinson bounds to better handle systems which lack translation invariance, we determine the extent to which &quot;weak links&quot; suppress operator growth in disordered one-dimensional spin chains. In particular, we prove that ballistic growth is impossible when the distribution of coupling strengths μ(J) has a sufficiently heavy tail at small J, and identify the correct dynamical exponent to use instead. Furthermore, through a detailed analysis of the special case in which the couplings are genuinely random and independent, we find that the standard formulation of Lieb-Robinson bounds is insufficient to capture the complexity of the dynamics -- we must distinguish between bounds which hold for all sites of the chain and bounds which hold for a subsequence of sites, and we show by explicit example that these two can have dramatically different behaviors. All the same, our result for the dynamical exponent is tight, in that we prove by counterexample that there cannot exist any Lieb-Robinson bound with a smaller exponent. We close by discussing the implications of our results, both major and minor, for numerous applications ranging from quench dynamics to the structure of ground states.</p>10aDisordered Systems and Neural Networks (cond-mat.dis-nn)10aFOS: Physical sciences10aMathematical Physics (math-ph)10aQuantum Physics (quant-ph)1 aBaldwin, Christopher, L.1 aEhrenberg, Adam1 aGuo, Andrew, Y.1 aGorshkov, Alexey, V.  uhttps://arxiv.org/abs/2208.05509