Abstract:
We show that the ground states of the three-dimensional XXZ Heisenberg ferromagnet with a 111 interface have excitations localized in a subvolume of linear size R with energies bounded by O(1/R 2). As part of the proof we show the equivalence of ensembles for the 111 interface states in the following sense: In the thermodynamic limit the states with fixed magnetization yield the same expectation values for gauge invariant local observables as a suitable grand canonical state with fluctuating magnetization. Here, gauge invariant means commuting with the total third component of the spin, which is a conserved quantity of the Hamiltonian. As a corollary of equivalence of ensembles we also prove the convergence of the thermodynamic limit of sequences of canonical states (i.e., with fixed magnetization).
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Received: 30 August 1999 / Accepted: 5 January 2000
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Bolina, O., Contucci, P., Nachtergaele, B. et al. Finite-Volume Excitations of the¶111 Interface in the Quantum XXZ Model. Comm Math Phys 212, 63–91 (2000). https://doi.org/10.1007/s002200000192
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DOI: https://doi.org/10.1007/s002200000192