Two-dimensional quantum XY model with ring exchange and external field

We present the zero-temperature phase diagram of a square lattice quantum spin-½ X Y model with four-site ring exchange in a uniform external magnetic field. Using quantum Monte Carlo techniques, we identify various quantum phase transitions between the XY order, striped or valence bond solid, staggered Neel anti-ferromagnet and fully polarized ground states of the model. We find no evidence for a quantum spin liquid phase.