Bosonic mean-field theory of quantum Heisenberg spin systems: Bose condensation and magnetic order

We discuss the mean-field approach to the quantum Heisenberg ferromagnet and antiferromagnet on bipartite lattices using the Schwinger boson representation, with the constraints imposed on the average. The low-dimensional results of Arovas and Auerbach [Phys. Rev. B. 38, 316 (1988)] are derived simply by using a Hartree-Fock decomposition and the Peierls variational principle. We study the models below their critical temperatures in three dimensions (and at zero temperature in d=2 dimensions) by identifying magnetic ordering with Bose condensation of the Schwinger bosons. This novel interpretation enables us to compute the low-temperature (in the ordered regime) thermodynamic properties and dispersion relations, which agree with the results of spin-wave theory. We also extract critical properties that are related to those of the spherical model. A brief discussion of the limitations of the approach is also presented.