Field theory for generalized Shastry-Sutherland models

We consider the bosonic dimer representation for generalized Shastry-Sutherland models that have the same symmetries as the original Shastry-Sutherland model and preserve the exact dimer eigenstate. Various phases with differing types of magnetic order are found within mean-field theory for the corresponding low-energy effective dimer field theory. Transitions are allowed between any of these mean-field phases, which are dimer Bose condensates, and with the dimer phase, which is the dimer Bose vacuum. The Néel state, absent from this mean-field study, is described as a bosonic Mott insulator induced by the coupling to the underlying lattice. Moreover, dimer Bose condensates with local Néel order are found to be unstable to spiral states. Instead of a direct phase transition between the dimer and the Néel phases, we propose an intermediate weakly incommensurate spin-density wave phase. The stability of the mean-field transitions is studied by renormalization techniques in $d=2,$ the upper critical dimension. While the transition from the Néel phase is found to be stable, the transition point from the dimer phase is not perturbatively accessible. We argue that the latter renormalization results point to the possibility of an intermediate phase of a different kind.