Phase transitions in the "easy plane" JQ model

We study the JQ model on the square lattice after adding to it “easy plane” terms that explicitly break the SU(2) symmetry of the original model. The Néel to VBS transition is believed to be continuous for the full SU(2) symmetric model. In the easy-plane limit, this model was shown to have a first order transition between the superfluid and the VBS phases. We use Stochastic Series Expansion Quantum Monte Carlo to investigate the nature of this transition for various strengths of this easy-plane anisotropy. We find that the first order nature of the transition weakens as we weaken the strength of the easy-plane interaction. However, we find no evidence that this transition becomes continuous before the SU(2) symmetric point.