Nearly Linear Light Cones in Long-Range Interacting Quantum Systems

In nonrelativistic quantum theories with short-range Hamiltonians, a velocity v can be chosen such that the influence of any local perturbation is approximately confined to within a distance r until a time t ∼r /v , thereby defining a linear light cone and giving rise to an emergent notion of locality. In systems with power-law (1 /r^α) interactions, when α exceeds the dimension D , an analogous bound confines influences to within a distance r only until a time t ∼(α /v )log r , suggesting that the velocity, as calculated from the slope of the light cone, may grow exponentially in time. We rule out this possibility; light cones of power-law interacting systems are bounded by a polynomial for α >2 D and become linear as α →∞. Our results impose strong new constraints on the growth of correlations and the production of entangled states in a variety of rapidly emerging, long-range interacting atomic, molecular, and optical systems.