TY - JOUR T1 - Nearly-linear light cones in long-range interacting quantum systems JF - Physical Review Letters Y1 - 2015 A1 - Michael Foss-Feig A1 - Zhe-Xuan Gong A1 - Charles W. Clark A1 - Alexey V. Gorshkov AB - In non-relativistic 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 $t \sim r/v$, thereby defining a linear light cone and giving rise to an emergent notion of locality. In systems with power-law ($1/r^{\alpha}$) interactions, when $\alpha$ exceeds the dimension $D$, an analogous bound confines influences to within a distance $r$ only until a time $t\sim(\alpha/v)\log r$, 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 algebraic for $\alpha>2D$, becoming linear as $\alpha\rightarrow\infty$. 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. VL - 114 U4 - 157201 UR - http://arxiv.org/abs/1410.3466v1 CP - 15 J1 - Phys. Rev. Lett. U5 - 10.1103/PhysRevLett.114.157201 ER -