Simulations of quantum XXZ models on two-dimensional frustrated lattices

We report recent progress in the study of a particular class of spin 1/2 XXZ model on two-dimensional lattices with frustrated diagonal and unfrustrated off-diagonal interactions. Quantum Monte Carlo simulations can be constructed without a sign problem; however, they require non-trivial algorithmic advances in order to combat freezing tendencies. We discuss results obtained using these techniques, in particular the discovery of unusual bulk quantum phases, studies of quantum criticality, and the continuing search for exotic physics in these models