Abstract
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 [O_i(t),O_j]t^2D+1(R-vt)^-α with v=O(1) for two arbitrary operators O_i and O_j 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 α<2D+1. In the regime of α>2D+1, our result characterizes the best general constraints on the information spreading.