New approaches to the quantum Heisenberg models: Schwinger boson representations (invited)

Abstract

Schwinger boson representations allow us to study ferromagnetic and antiferromagnetic Heisenberg models in a rotationally invariant formulation. The large-N SU (N) Heisenberg models are approximated by the Schwinger boson mean-field theory (SBMFT). In most cases, even for N=2 (the physical model), the SBMFT is surprisingly successful: We review recent comparisons with numerical results, spin-wave theory, and renormalization group analysis of the nonlinear sigma model. The mean-field theory, like the nonlinear sigma model, does not include the effects of topological Berry phases, which can appear in the antiferromagnetic spin liquid phases.