Criticality in quantum triangular antiferromagnets via fermionized vortices

TL;DR

This paper develops a fermionized-vortex approach to study criticality in frustrated quantum antiferromagnets, revealing a duality between QED3 and O(4) symmetric field theories, and predicts new critical phenomena.

Contribution

It introduces a novel fermionized-vortex method for integer-spin triangular antiferromagnets, connecting QED3 with O(4) criticality and providing verifiable predictions.

Findings

QED3 with SU(2) flavor symmetry describes the multicritical point.

QED3 is dual to O(4) symmetric Phi^4 theory.

Connection established with fractional quantum Hall state interpretation.

Abstract

We revisit two-dimensional frustrated quantum magnetism from a new perspective, 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.