Abstract
We show that in the ground states of the infinite-volume limits of both the spin-1/2 anisotropic antiferromagnetic Heisenberg model (in dimensions d⩾2), and the ferromagnetic Ising model in a strong transverse field (in dimensions d⩾1) there is an interval in the spectrum above the mass gap which contains a continuous band of energy levels. We use the methods of Bricmont and Fröhlich to develop our expansions, as well as a method of Kennedy and Tasaki to do the expansions in the quantum mechanical limit. Where the expansions converge, they are then shown to have spectral measures which have absolutely continuous parts on intervals above the mass gaps.
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Pokorny, M. Continuous spectrum in the ground state of two spin-1/2 models in the infinite-volume limit. J Stat Phys 72, 381–403 (1993). https://doi.org/10.1007/BF01048055
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DOI: https://doi.org/10.1007/BF01048055