Quantum criticality in ``easy-plane'' SU($N$) spin model

We investigate a two dimensional quantum spin model with ``easy-plane'' SU($N$) anisotropy which describes an $N-1$ component superfluid of hard-core bosons. This model exhibits a transition from a magnetically ordered state, corresponding to superfluid order of the bosons, to a non-magnetic state with broken lattice translation symmetry (a valence bond solid). It has been shown previously that the fully SU($N$) symmetric version of this model exhibits a continuous phase transition consistent with the scenario of deconfined quantum criticality. Using quantum Monte Carlo techniques we study the critical properties in the ``easy-plane'' case.