Chiral spin liquid in a two-dimensional helical $XY$ magnet with two chiral order parameters

The critical properties of an $XY$ helimagnet on a square lattice with two chiral order parameters are studied by Monte Carlo simulations. This model is a modification of the $J_1$–$J_2$–$J_3$ model with $J_2=0$. The case of different third range order interactions $J_3$ are considered, $J_3^a\ne J_3^b$ . A first order transition is found away from the Lifshitz points $4J_3^a=J_1$ and $4J_3^b=J_1$. It is pointed out that a chiral spin liquid phase possibly exists near the Lifshitz points.