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Hierarchy of Linear Light Cones with Long-Range Interactions
Physical Review X ( IF 12.5 ) Pub Date : 2020-07-13 , DOI: 10.1103/physrevx.10.031009
Minh C. Tran , Chi-Fang Chen , Adam Ehrenberg , Andrew Y. Guo , Abhinav Deshpande , Yifan Hong , Zhe-Xuan Gong , Alexey V. Gorshkov , Andrew Lucas

In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently separated spacetime points approximately commute—given a many-body state |ψ, Ox(t)Oy|ψOyOx(t)|ψ with arbitrarily small errors—so long as |xy|vt, where v is finite. Yet, most nonrelativistic physical systems realized in nature have long-range interactions: Two degrees of freedom separated by a distance r interact with potential energy V(r)1/rα. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: At the same α, some quantum information processing tasks are constrained by a linear light cone, while others are not. In one spatial dimension, this linear light cone exists for every many-body state |ψ when α>3 (Lieb-Robinson light cone); for a typical state |ψ chosen uniformly at random from the Hilbert space when α>52 (Frobenius light cone); and for every state of a noninteracting system when α>2 (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones—and their tightness—also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that universal quantum state transfer, as well as many-body quantum chaos, is bounded by the Frobenius light cone and, therefore, is poorly constrained by all Lieb-Robinson bounds.

中文翻译:

具有长距离交互作用的线性光锥的层次结构

在具有局部相互作用的量子多体系统中,量子信息和纠缠不能散布在线性光锥之外,线性光锥以类似于光速的出射速度扩展。考虑到多体状态,在足够分离的时空点上的本地操作大约通勤|ψØXŤØÿ|ψØÿØXŤ|ψ 只要有很小的错误,只要 |X-ÿ|vŤ,在哪里 v是有限的。然而,自然界中实现的大多数非相对论物理系统都具有远程相互作用:两个自由度相隔一段距离[R 与势能相互作用 V[R1个/[Rα。在具有长距离交互作用的系统中,我们严格建立线性光锥层次结构α,某些量子信息处理任务受线性光锥约束,而另一些则不受约束。在一个空间维度上,这种线性光锥存在于每个多体状态|ψ 什么时候 α>3(Lieb-Robinson光锥);对于典型状态|ψ 从希尔伯特空间中随机选择均匀 α>52(Frobenius灯锥); 对于非交互系统的每个状态,当α>2(免费的光锥)。这些界限适用于与时间有关的系统,并且在次代数改进之前是最佳的。我们关于Lieb-Robinson和自由光锥的定理及其紧密性也可以推广到任意尺寸。我们讨论了边界对连接的相关器和拓扑顺序的增长,间隙系统中的相关性聚类以及具有远程交互作用的系统的数字仿真的影响。此外,我们证明了普遍量子态转移以及多体量子混沌受Frobenius光锥限制,因此受所有Lieb-Robinson限制的约束较弱。
更新日期:2020-07-13
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