  We study quasiparticle excitations for quantum spin chains with long-range
interactions using variational matrix product state techniques. It is confirmed
that the local quasiparticle ansatz is able to capture those excitations very
accurately, even when the correlation length becomes very large and in the case
of topological nontrivial excitation such as spinons. It is demonstrated that
the breaking of the Lieb-Robinson bound follows from the appearance of cusps in
the dispersion relation, and evidence is given for a crossover between
different quasiparticles as the long-range interactions are tuned.
