Lieb-Robinson Light Cone for Power-Law Interactions

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(a) at distance r? Here, we present a definitive answer to this question for all exponents a > 2d and all spatial dimensions d. Schematically, information takes time at least r(min{1,a-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.

Automated summary

The Lieb-Robinson theorem establishes finite information propagation velocity in quantum systems on a lattice with nearest-neighbor interactions. In quantum systems with power-law interactions, the speed limits of information propagation have been definitively answered for all exponents a > 2d and spatial dimensions d. Information propagation takes at least time r(min{1,a-2d}) to cover a distance r, with recent state transfer protocols asserting this boundary, concluding a long quest for optimal Lieb-Robinson bounds in quantum information dynamics with power-law interactions.