Quasiparticles in quantum spin chains with long-range interactions

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.