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Protected quasi-locality in quantum systems with long-range interactions

We study the out-of-equilibrium dynamics of quantum systems with long-range interactions. Two different models describing, respectively, interacting lattice bosons and spins are considered. Our study relies on a combined approach based on accurate many-body numerical calculations as well as on a quasiparticle microscopic theory. For sufficiently fast decaying long-range potentials, we find that the quantum speed limit set by the long-range Lieb-Robinson bounds is never attained and a purely ballistic behavior is found. For slowly decaying potentials, a radically different scenario is observed. In the bosonic case, a remarkable local spreading of correlations is still observed, despite the existence of infinitely fast traveling excitations in the system. This is in marked contrast to the spin case, where locality is broken. We finally provide a microscopic justification of the different regimes observed and of the origin of the protected locality in the bosonic model.