  In recent experiments with ion traps, long-range interactions were associated
with the exceptionally fast propagation of perturbation, while in some
theoretical works they have also been related with the suppression of
propagation. Here, we show that such apparently contradictory behavior is
caused by a general property of long-range interacting systems, which we name
"Cooperative Shielding". It refers to shielded subspaces that emerge as the
system size increases and inside of which the evolution is unaffected by
long-range interactions for a long time. As a result, the dynamics strongly
depends on the initial state: if it belongs to a shielded subspace, the
spreading of perturbation satisfies the Lieb-Robinson bound and may even be
suppressed, while for initial states with components in various subspaces, the
propagation may be quasi-instantaneous. We establish an analogy between the
shielding effect and the onset of quantum Zeno subspaces. The derived effective
Zeno Hamiltonian successfully describes the short-ranged dynamics inside the
subspaces up to a time scale that increases with system size. Cooperative
Shielding can be tested in current experiments with trapped ions.
