Oscar Bolina, Pierluigi Contucci, Bruno Nachtergaele, Shannon Starr
Finite-volume excitations of the 111 interface in the quantum XXZ modelLatex
(212K, Latex, 5 figures in eps format included using epsfig)

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).