Spread of correlations in long-range interacting quantum systems

The nonequilibrium response of a quantum many-body system defines its fundamental transport properties and how initially localized quantum information spreads. However, for long-range-interacting quantum systems little is known. We address this issue by analyzing a local quantum quench in the long-range Ising model in a transverse field, where interactions decay as a variable power law with distance alpha r(-alpha), alpha > 0. Using complementary numerical and analytical techniques, we identify three dynamical regimes: short-range-like with an emerging light cone for alpha > 2, weakly long range for 1 < alpha < 2 without a clear light cone but with a finite propagation speed of almost all excitations, and fully nonlocal for alpha < 1 with instantaneous transmission of correlations. This last regime breaks generalized Lieb-Robinson bounds and thus locality. Numerical calculation of the entanglement spectrum demonstrates that the usual picture of propagating quasiparticles remains valid, allowing an intuitive interpretation of our findings via divergences of quasiparticle velocities. Our results may be tested in state-of-the-art trapped-ion experiments.