@article {1178, title = {Nearly-linear light cones in long-range interacting quantum systems}, journal = {Physical Review Letters}, volume = {114}, year = {2015}, month = {2015/04/13}, pages = {157201}, abstract = { 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. }, doi = {10.1103/PhysRevLett.114.157201}, url = {http://arxiv.org/abs/1410.3466v1}, author = {Michael Foss-Feig and Zhe-Xuan Gong and Charles W. Clark and Alexey V. Gorshkov} }