We present the zero-temperature phase diagram of a square lattice quantum spin-1/2 $\mathrm{XY}$ 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 $\mathrm{XY}$ order, striped or valence bond solid, staggered Néel antiferromagnet and fully polarized ground states of the model. We find no evidence for a quantum spin liquid phase.

• Received 6 November 2003

DOI:https://doi.org/10.1103/PhysRevB.69.100408