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^{-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-v[over ¯]t)^{-α} with v[over ¯]=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 α2D+1, our result characterizes the best general constraints on the information spreading.