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

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 - with distance R. We prove the existence of the linear light cone for > 2D 1 (D, the spatial dimension), where we obtain the Lieb-Robinson bound as kO i t; O j k t 2D1 R -vt - with v O1 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 < 2D 1. In the regime of > 2D 1, our result characterizes the best general constraints on the information spreading.