Asymptotic Observables in Gapped Quantum Spin Systems

Abstract

This paper gives a construction of certain asymptotic observables (Araki-Haag detectors) in ground state representations of gapped quantum spin systems. The construction is based on general assumptions which are satisfied e.g. in the Ising model in strong transverse magnetic fields. We do not use the method of propagation estimates, but exploit instead compactness of the relevant propagation observables at any fixed time. Implications for the problem of asymptotic completeness are briefly discussed.