Duality argument for the chiral-nematic phase of planar spins

A duality argument for the recently discovered chiral-nematic phase of the XY model in a triangular lattice is presented. We show that a new Ising variable naturally emerges in mapping the antiferromagnetic J₁.-J₂ classical XY spin Hamiltonian onto an appropriate Villain model on a triangular lattice. The new variable is the chirality degree of freedom, which exists in addition to the usual vortex variables, in the dual picture. Elementary excitations and the associated phase transition of the Ising degrees of freedom are discussed in some detail.