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Strictly linear light cones in long-range interacting systems of arbitrary dimensions
Physical Review X ( IF 11.6 ) Pub Date : 
Tomotaka Kuwahara, Keiji Saito

In locally interacting quantum many-body systems, the velocity of information propagation is finitely bounded and a linear light cone can be defined. Outside the light cone, the amount of information rapidly decays with distance. When systems have long-range interactions, it is highly nontrivial whether such a linear light cone exists. Herein, we consider generic long-range interacting systems with decaying interactions, such as Rα with distance R. We prove the existence of the linear light cone for α>2D+1 (D: the spatial dimension), where we obtain the Lieb–Robinson bound as [Oi(t),Oj]t2D+1(Rvt)α with v=𝒪(1) for two arbitrary operators Oi and Oj separated by a distance R. Moreover, we provide an explicit quantum-state transfer protocol that achieves the above bound up to a constant coefficient and violates the linear light cone for α2D+1, our result characterizes the best general constraints on the information spreading.

中文翻译:

任意尺寸的远程相互作用系统中的严格线性光锥

在局部相互作用的量子多体系统中,信息传播的速度受到有限的限制,并且可以定义线性光锥。在光锥外部,信息量随距离迅速衰减。当系统具有远距离相互作用时,是否存在这样的线性光锥是非常重要的。在这里,我们考虑具有衰减相互作用的通用远程相互作用系统,例如[R-α 与距离 [R。我们证明存在线性光锥α>2d+1个d:空间维度),在这里我们得到的Lieb-Robinson界为 [Ø一世ŤØĴ]Ť2d+1个[R-vŤ-αv=𝒪1个 对于两个任意运算符 Ø一世ØĴ 相隔一段距离 [R。此外,我们提供了一个明确的量子态转移协议,该协议可实现上述约束,直至达到一个恒定的系数,并且违反了线性光锥α2d+1个,我们的结果表征了信息传播的最佳一般约束。
更新日期:2020-07-13
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