Lieb-Robinson-Type Bounds for Quantum Systems with Strongly Long-Range Interactions

We prove bounds on the rate of correlation-spreading in long-range quantum lattice systems---specifically those with interaction strengths that decay as a power-law r^-α in the distance r. Such long-range interacting systems include dipolar spin interactions in neutral atoms and molecules, as well as tunable spin-spin interactions in trapped ions. For strongly long-range Hamiltonians with α less than the lattice dimension, we give two new Lieb-Robinson-type bounds. First, we prove a tight bound on free-particle Hamiltonians with long-range hopping terms and provide a protocol for quantum state transfer that saturates the bound. We also prove a general bound for interacting Hamiltonians that gives the smallest causal region compared to existing general bounds. This latter result gives a lower bound on the fastest possible scrambling time for a long-range interacting system.