  The non-equilibrium 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 $\propto r^{-\alpha}$, $\alpha>0$. 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 non-local 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
quasi-particles remains valid, allowing an intuitive interpretation of our
findings via divergences of quasi-particle velocities. Our results may be
tested in state-of-the-art trapped-ion experiments.
