We present quantum Monte Carlo simulation results on a quantum $S=1∕2XY$ model with ring exchange (the $J\text{−}K$ model) on a three-dimensional simple cubic lattice. We first characterize the ground-state properties of the pure $XY$ model, obtaining estimations for the energy, spin stiffness, and spin susceptibility at $T=0$ in the superfluid phase. With the ring exchange, we then present simulation data on small lattices which suggest that the superfluid phase persists to very large values of the ring exchange $K$, without the signatures of a phase transition. We comment on the consequences of this result for the search for various exotic phases in three dimensions.

• Received 24 August 2004

DOI:https://doi.org/10.1103/PhysRevB.71.094511