Strictly Linear Light Cones in Long-Range Interacting Systems of Arbitrary Dimensions

In locally interacting quantum many-body systems, the velocity of information propagation is finitely hounded, 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-alpha with distance R. We prove the existence of the linear light cone for alpha > 2D + 1 (D, the spatial dimension), where we obtain the Lieb-Robinson bound as parallel to[O-i, O-j]parallel to less than or similar to t(2D+1) (R - (v) over bart)(-alpha) with (v) over bar = O(1) for two arbitrary operators O-i 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 alpha < 2D + 1. In the regime of alpha > 2D + 1, our result characterizes the best general constraints on the information spreading.