Emergent locality in systems with power-law interactions

In generic systems with local interactions transport is diffusive and information propagates inside a quasicausal "light-cone" parametrized by a constant velocity known as the Lieb-Robinson velocity. Introducing long-range interactions, should intuitively enhance transport by long-range hops, and deform the linear "light-cones," into a superballistic form. Using two numerically exact techniques I will show that this is not the case for a number of generic one-dimensional systems. All studied systems, for sufficiently short-range interactions, show universal behaviour of asymptotically emergent locality and a unique composite transport comprised of diffusive and superdiffusive features.