On Polynomial Lieb-Robinson Bounds for the XY Chain in a Decaying Random Field

We consider the isotropic XY quantum spin chain in a random external field in the z direction, with single site distributions given by i.i.d. random variables times the critical decaying envelope j^(−1/2). Our motivation is the study of many-body localization. We investigate transport properties in terms of polynomial Lieb–Robinson (PLR) bounds. We prove a zero-velocity PLR bound for large disorder strength λ and for small λ we show a partial converse, which suggests the existence of a transition to non-trivial transport in the model