Finite-Volume Excitations of the¶111 Interface in the Quantum XXZ Model |
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Authors: | Oscar Bolina Pierluigi Contucci Bruno Nachtergaele Shannon Starr |
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Institution: | Department of Mathematics, University of California, Davis, CA 95616-8633, USA.?E-mail:bolina@math.ucdavis.edu; contucci@math.ucdavis.edu; bxn@math.ucdavis.edu;?sstarr@math.ucdavis.edu, US
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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/R2). 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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