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Motivated by the anisotropic long-range nature of the interactions betweencold dipolar atoms or molecules in an optical lattice, we study the anisotropicquantum Heisenberg model with Curie-Weiss-type long-range interactions. Absenceof a heat bath in optical lattice experiments suggests a study of this modelwithin the microcanonical ensemble. The microcanonical entropy is calculatedanalytically, and nonequivalence of microcanonical and canonical ensembles isfound for a range of anisotropy parameters. From the shape of the entropy itfollows that the Curie-Weiss Heisenberg model is indistinguishable from theCurie-Weiss Ising model in canonical thermodynamics, although theirmicrocanonical thermodynamics differs. Qualitatively, the observed features ofnonequivalent ensembles are expected to be relevant for long-range quantum spinsystems realized in optical lattice experiments.

Nonequivalence of ensembles for long-range quantum spin systems in optical lattices