  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).
