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, under a CP 1 constraint broken vertical bar z1|(2) + | z(2)|(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 CP1 model completely suppresses the phase transition in the O(3) universality class of the CP1 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.