Nematic and chiral order for planar spins on a triangular lattice

We propose a variant of the antiferromagnetic XY model which includes a biquadratic (J2) as well as the quadratic (J1) interaction on the triangular lattice. The phase diagram for large J2/J1 exhibits a phase with coexisting quasi-long-range nematic, and long-ranged vector spin chirality orders in the absence of magnetic order, which qualifies our model as the first instance of a classical spin model that exhibits a vector chiral spin liquid phase. The interplay of nematic and spin chirality orders is discussed. A variety of critical properties are derived by means of Monte Carlo simulation.