Two-dimensional quantumXYmodel with ring exchange and external field

We present the zero-temperature phase diagram of a square lattice quantum spin-1/2 XY 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 N\'eel antiferromagnet and fully polarized ground states of the model. We find no evidence for a quantum spin liquid phase.