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

Abstract

We consider a lattice model of two complex scalar matter fields ${z}_{a},\phantom{\rule{0.16em}{0ex}}a=1,2$, under a ${\mathbb{CP}}^{1}$ constraint $|{z}_{1}{|}^{2}+{|{z}_{2}|}^{2}=1$, 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 ${\mathbb{CP}}^{1}$ model completely suppresses the phase transition in the $\mathrm{O}(3)$ 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.