Criticality in quantum triangular antiferromagnets via fermionized vortices

We reexamine two-dimensional frustrated quantum magnetism with the aim of exploring new critical points and critical phases. We study easy-plane triangular antiferromagnets using a dual vortex approach, fermionizing the vortices with a Chern-Simons field. Herein we develop this technique for integer-spin systems which generically exhibit a simple paramagnetic phase as well as magnetically ordered phases with coplanar and collinear spin order. Within the fermionized-vortex approach, we derive a low-energy effective theory containing Dirac fermions with two flavors minimally coupled to a U(1) and a Chern-Simons gauge field. At criticality we argue that the Chern-Simons gauge field can be subsumed into the U(1) gauge field, and up to irrelevant interactions one arrives at quantum electrodynamics in $2+1$ dimensions (QED3). Moreover, we conjecture that critical QED3 with full SU(2) flavor symmetry describes the O(4) multicritical point of the spin model where the paramagnet and two magnetically ordered phases merge. The remarkable implication is that QED3 with flavor SU(2) symmetry is dual to ordinary critical ${\Phi }^4$ field theory with O(4) symmetry. This leads to a number of unexpected, verifiable predictions for QED3. A connection of our fermionized-vortex approach with the dipole interpretation of the $\nu =1∕2$ fractional quantum Hall state is also demonstrated. The approach introduced in this paper will be applied to spin-$1∕2$ systems in a forthcoming publication.