New easy-plane $\mathbb{CP}^{N-1}$ fixed points

Understand

We study fixed points of the easy-plane $\mathbb{CP}^{N-1}$ field theory by combining quantum Monte Carlo simulations of lattice models of easy-plane SU($N$) superfluids with field theoretic renormalization group calculations, by using ideas of deconfined criticality.

• From our simulations, we present evidence that at small $N$ our lattice model has a first order phase transition which progressively weakens as $N$ increases, eventually becoming continuous for large values of $N$.
• Renormalization group calculations in $4-\epsilon$ dimensions provide an explanation of these results as arising due to the existence of an $N_{ep}$ that separates the fate of the flows with easy-plane anisotropy.
• When $N<N_{ep}$ the renormalization group flows to a discontinuity fixed point and hence a first order transition arises.