Schwinger boson approach to magnetically ordered quantum magnets

The quest for quantum spin liquids is producing a large number of magnetically ordered quantum magnets that exhibit anomalies in their dynamical spin structure factor. These anomalies include a strong renormalization of the single-magnon bands and a broad continuum of excitations, whose integrated spectral weight is larger than the weight of the single-magnon peaks. These observations call for novel approaches that can properly capture the effect of strong quantum fluctuations. By considering a Schwinger boson theory (large-N approach) beyond the saddle-point approximation (N = ∞), we demonstrate that the inclusion of 1/N corrections is strictly necessary to remove unphysical modes (single-spinon poles) and to capture the true magnon modes, which emerge as two-spinon bound states (poles of the RPA propagator). Moreover, we show that for each Feynman diagram there is a counter-diagram that removes the unphysical single-spinon poles. The counter-diagrams are different for collinear and non-collinear orderings. Based on these results, we demonstrate that the large-N approach can exactly reproduce the spin-wave theory in the large-S limit.