Finite-volume excitations of the 111 interface in the quantum XXZ model

Details Finite-volume excitations of the 111 interface in the quantum XXZ model Finite-volume excitations of the 111 interface in the quantum XXZ model

1999-08-19

arxiv.org/abs/math-ph/9908018v1

Comm. Math. Phys., 212 (2000) 63-91

Physics

Mathematical Physics

36 pages, 5 figures

Scientific paper

10.1007/s002200000192

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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