Asymptotic observables in gapped quantum spin systems

TL;DR

This paper constructs asymptotic observables in gapped quantum spin systems' ground states, offering a new approach that avoids propagation estimates and has implications for asymptotic completeness.

Contribution

It introduces a novel construction of Araki-Haag detectors in gapped quantum spin systems without using propagation estimates.

Findings

Construction applies to models like the Ising model in strong transverse fields

Uses compactness of propagation observables at fixed times

Discusses implications for asymptotic completeness

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.