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Strictly linear light cones in long-range interacting systems of arbitrary dimensions
Physical Review X ( IF 12.577 ) 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 R−α 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(R−v‾t)−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.
更新日期:2020-07-10

 

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