1999/08/19 by Oscar Bolina, Pierluigi Contucci, Bruno Nachtergaele +1 · 1 citation
Mathematics · Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum many-body systems #Theoretical and Computational Physics #cond-mat.stat-mech #math-ph #math.MP #msc:82B10 #msc:82B24 #msc:82D40
paper · pdf · doi:10.1007/s002200000192
published as Comm. Math. Phys., 212 (2000) 63-91 · 36 pages, 5 figures
arxiv created 1999/08/19 · openalex publication_date 2000/06/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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).