Phase diagram of easy-plane deformations of SU(N) magnets

We consider Hamiltonians of SU($N$) quantum magnets with easy-plane deformations, leaving a U(1) rotation symmetry about each of the $N-1$ diagonal generators and a discrete $Z_{N}$ symmetry. For $N=2$ our model reduces to the XY model and can hence be considered as a larger-$N$ generalization of this well-studied model. We present numerical data from quantum Monte Carlo simulations which allows us to map the phase diagram of these models as a function of $N$, including both two-spin and four-spin interactions.