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

TL;DR

This paper studies transport in a disordered quantum spin chain, proving bounds that suggest localization at high disorder and possible transport at low disorder, advancing understanding of many-body localization phenomena.

Contribution

It establishes polynomial Lieb-Robinson bounds for the XY chain with decaying random fields, revealing different transport regimes depending on disorder strength.

Findings

Zero-velocity PLR bound at large disorder

Partial converse indicating possible transport at small disorder

Insights into many-body localization in disordered quantum systems

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.