  Quasiparticle properties of quantum magnets with long-range interactions are
investigated by high-order linked-cluster expansions in the thermodynamic
limit. It is established that perturbative continuous unitary transformations
on white graphs are a promising and flexible approach to treat long-range
interactions in quantum many-body systems. We exemplify this scheme for the
one-dimensional transverse-field Ising chain with long-range interactions. For
this model the elementary Quasiparticle gap is determined allowing to access
the quantum-critical regime including critical exponents and multiplicative
logarithmic corrections for the ferro- and antiferromagnetic case.
