On polynomial Lieb-Robinson bounds for the XY chain in a decaying random field

Abstract

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 $\lambda$ and for small $\lambda$ we show a partial converse, which suggests the existence of non-trivial transport in the model.

16 pages

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• Local integrals of motion and the stability of many-body localisation in Wannier-Stark potentials
• On Lieb-Robinson bounds for a class of continuum fermions
• A Lieb-Robinson bound for quantum spin chains with strong on-site impurities
• Sub-ballistic operator growth in spin chains with heavy-tailed random fields
• Decay of Complex-time Determinantal and Pfaffian\ Correlation Functionals in Lattices