Lieb-Robinson Light Cone for Power-Law Interactions

Abstract

The Lieb-Robinson theorem states that information propagates with a finite velocity in quantum systems on a lattice with nearest-neighbor interactions. What are the speed limits on information propagation in quantum systems with power-law interactions, which decay as $1/r^{\alpha }$ at distance $r$? Here, we present a definitive answer to this question for all exponents $\alpha >2d$ and all spatial dimensions $d$. Schematically, information takes time at least $r^{\min \{1,\alpha -2d\}}$ to propagate a distance $r$. As recent state transfer protocols saturate this bound, our work closes a decades-long hunt for optimal Lieb-Robinson bounds on quantum information dynamics with power-law interactions.