Title: On polynomial Lieb-Robinson bounds for the XY chain in a decaying random field Show Chinese title

Title: 关于XY链在衰减随机场中的多项式Lieb-Robinson界

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. Show Chinese abstract

Abstract: 我们研究了在一维各向同性的XY自旋链在外加随机磁场下的情形，其中随机场的方向为 $z$，单点分布由独立同分布的随机变量乘以临界衰减包络 $j^{-1/2}$给出。我们的动机来源于对多体局域化的研究。我们通过多项式Lieb-Robinson（PLR）界限来探讨输运性质。我们证明了当无序强度 $\lambda$较大时存在零速度的PLR界限；对于较小的 $\lambda$，我们展示了部分逆命题，这表明该模型中可能存在非平凡的输运现象。