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

TL;DR

This paper combines quantum Monte Carlo simulations and renormalization group analysis to explore phase transitions in easy-plane $ ext{CP}^{N-1}$ models, revealing a transition from first order to continuous as N increases, and identifying a new fixed point for large N.

Contribution

It provides the first combined numerical and theoretical evidence for a new easy-plane $ ext{CP}^{N-1}$ fixed point and clarifies the role of N in the nature of phase transitions.

Findings

First order transition at small N weakens with increasing N.

Transition becomes continuous for large N.

Identification of a critical N separating different flow behaviors.

Abstract

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. On the other hand, for $N > N_{ep}$ the flows are to a new easy-plane $\mathbb{CP}^{N-1}$ fixed point that describes the quantum criticality in the lattice model at large $N$. Our lattice model at its critical point thus gives efficient numerical access to a new strongly coupled gauge-matter field theory.