  We consider translation invariant gapped quantum spin systems satisfying the
Lieb-Robinson bound and containing single-particle states in a ground state
representation. Following the Haag-Ruelle approach from relativistic quantum
field theory, we construct states describing collisions of several particles,
and define the corresponding $S$-matrix. We also obtain some general
restrictions on the shape of the energy-momentum spectrum. For the purpose of
our analysis we adapt the concepts of almost local observables and
energy-momentum transfer (or Arveson spectrum) from relativistic QFT to the
lattice setting. The Lieb-Robinson bound, which is the crucial substitute of
strict locality from relativistic QFT, underlies all our constructions. Our
results hold, in particular, in the Ising model in strong transverse magnetic
fields.
