Fate of CPN-1 Fixed Points with q Monopoles

We present an extensive quantum Monte Carlo study of the Neel to valence-bond solid (VBS) phase transition on rectangular-and honeycomb-lattice SU(N) antiferromagnets in sign-problem-free models. We find that in contrast to the honeycomb lattice and previously studied square-lattice systems, on the rectangular lattice for small N, a first-order Neel-VBS transition is realized. On increasing N >= 4, we observe that the transition becomes continuous and with the same universal exponents as found on the honeycomb and square lattices (studied here for N 5, 7, 10), providing strong support for a deconfined quantum critical point. Combining our new results with previous numerical and analytical studies, we present a general phase diagram of the stability of CPN-1 fixed points with q monopoles.