Duality Argument for the Chiral-Nematic Phase of Planar Spins

TL;DR

This paper introduces a duality approach to analyze the chiral-nematic phase in a triangular lattice XY model, revealing a new Ising variable representing chirality and discussing its excitations and phase transition.

Contribution

It presents a novel duality argument that uncovers a new Ising variable linked to chirality in the XY model on a triangular lattice.

Findings

Emergence of a new Ising variable representing chirality

Analysis of elementary excitations in the dual picture

Discussion of phase transition of the Ising degrees of freedom

Abstract

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.