Berry phases, current lattices, and suppression of phase transitions in a lattice gauge theory of quantum antiferromagnets

We consider a lattice model of two complex scalar matter fields $z_{a}, a=1,2$underaCP1constraint$\abs{z_1}^2+\abs{z_2}^2=1$, minimally coupled to a compact gauge field, with an additional Berry phase term. This model has been the point of origin for 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 to 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=360. We show that the addition of a Berry phase term to the lattice $\text{CP}$-model suppresses the phase transition in the $\text{groupO}3$ universality class of the $\text{CP}$-model. The link-current formulation of the model is useful in identifying the mechanism by which the phase transition is suppressed.