Deconfined criticality in "easy-plane" SU($N$) anti-ferromagnets

Motivated by evidence for deconfined criticality in SU($N$) anti-ferromagnets, we investigate the phase diagram of these models in the case where the SU($N$) symmetry is reduced to rotations about the diagonal generators ("easy-plane" symmetry). We carry out extensive numerical simulations using quantum Monte Carlo, revealing a first-order magnetic to valence bond solid phase transition that becomes a continuous deconfined transition at large $N$. We support our numerical data by performing epsilon expansions of the easy-plane deformed $CP^{N-1}$ field theory near both the upper and lower critical dimensions. This renormalization group analysis shows that the symmetric deconfined fixed point is unstable in the presence of easy-plane anisotropy, resulting in a runaway flow for intermediate values of $N$ and a flow towards a stable easy-plane deconfined fixed point at large $N$, which is consistent with the critical behavior of our lattice models.