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Asymptotic Observables in Gapped Quantum Spin Systems

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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 the existence of the wave operators combined with the compactness of the relevant propagation observables at any fixed time. Implications for the problem of asymptotic completeness are briefly discussed.

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Authors and Affiliations

  1. Zentrum Mathematik, Technische Universität München, 85747, Garching, Germany

    Wojciech Dybalski

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  1. Wojciech Dybalski
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Correspondence to Wojciech Dybalski.

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Communicated by D. Buchholz, K. Fredenhagen, Y. Kawahigashi

Dedicated to the memory of Rudolf Haag

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Dybalski, W. Asymptotic Observables in Gapped Quantum Spin Systems. Commun. Math. Phys. 357, 231–248 (2018). https://doi.org/10.1007/s00220-017-2954-2

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  • DOI: https://doi.org/10.1007/s00220-017-2954-2

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