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 $z_a,a=1,2$ under a CP1 constraint $\abs{z_1}^2+\abs{z_2}^2=1$, 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 $\CP$-model suppresses the phase transition in the $\groupO{3}$ universality class of the $\CP$-model. The link-current formulation of the model is useful in identifying the mechanism by which the phase transition is suppressed.

12 pages, 9 figures. Published in Physical Review B

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• Coherent and dissipative dynamics at quantum phase transitions
• Lattice Abelian-Higgs model with noncompact gauge fields
• Scaling dimensions of higher-charge monopoles at deconfined critical points
• Higher-charge three-dimensional compact lattice Abelian-Higgs models
• Critical behaviors of lattice U(1) gauge models and three-dimensional Abelian-Higgs gauge field theory
• Three-dimensional Abelian and non-Abelian gauge Higgs theories
• Deconfinement transitions in three-dimensional compact lattice Abelian Higgs models with multiple-charge scalar fields
• Three-dimensional monopole-free CP${}^{N-1}$ models: Behavior in the presence of a quartic potential
• Strong-coupling critical behavior in three-dimensional lattice Abelian gauge models with charged $N$-component scalar fields and $SO(N)$ symmetry
• Sign-problem-free effective models of triangular lattice quantum antiferromagnets
• Scalar gauge-Higgs models with discrete Abelian symmetry groups