Quantum Monte Carlo simulations of spin 1/2 XY models with ring exchange

We present large-scale numerical simulations of several spin-1/2 XY models with four-site ring exchange, in the general class of the so-called J-K model. The Stochastic Series Expansion quantum Monte Carlo method employed in the simulations is described in detail. Physical results for ground state phases and phase transitions are presented for the two-dimensional square lattice J-K model in the presence and absence of uniform and staggered magnetic fields. The extension of the model to a three-dimensional cubic lattice is also discussed. Attempts are made throughout to address the question of whether "exotic" quantum ground state phenomena, such as spin liquid phases or deconfined critical points, occur in these models. Although the results presented are intriguing, no clear indication of exotic behavior is observed in the models studied.