We consider a lattice model of two complex scalar matter fields $z_a,a=1,2$, under a ${\mathbb{CP}}^1$ constraint $|z_1{|}^2+{\left|z_2\right|}^2=1$, minimally coupled to a compact gauge field, with an additional Berry-phase term. This model has been the origin of a large body of works addressing novel paradigms for quantum criticality, in particular “spin-quark” (spinon) deconfinement in $S=1/2$ quantum antiferromagnets. We map the model exactly onto a link-current model, which permits the use of classical worm algorithms to study the model in large-scale Monte Carlo simulations on lattices of size $L^3$, up to $L=512$. We show that the addition of a Berry-phase term to the lattice ${\mathbb{CP}}^1$ model completely suppresses the phase transition in the $\mathrm{O}\left(3\right)$ universality class of the ${\mathbb{CP}}^1$ model, such that the original spin system described by the compact gauge theory is always in the ordered phase. The link-current formulation of the model is useful in identifying the mechanism by which the phase transition from an ordered to a disordered state is suppressed.

• Received 12 March 2013

DOI:https://doi.org/10.1103/PhysRevB.88.094412