# Lieb-Robinson bounds, Arveson spectrum and Haag-Ruelle scattering theory for gapped quantum spin systems

December 09, 2014

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. Our results hold, in particular, in the Ising model in strong
transverse magnetic fields.

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