Abstract
We consider the kink (infinite volume nontranslationally invariant ground states) of the ferromagnetic XXZ models on the multi-dimensional lattices. We obtained the following results: (i) The pure states satisfying the local zero energy condition are necessarily product states. (ii) The Hamiltonian in the GNS representation of the kink has no gap between the ground-state eigenvalue and the rest of the spectra.
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Matsui, T. On the Spectra of the Kink for Ferromagnetic XXZ Models. Letters in Mathematical Physics 42, 229–239 (1997). https://doi.org/10.1023/A:1007396827804
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DOI: https://doi.org/10.1023/A:1007396827804