Possibility of a Topological Phase Transition in Two-dimensional RP³ Model

We study by large-scale Monte Carlo simulation the RP3 model, which can be regarded as an effective low-energy model of a triangular lattice Heisenberg antiferromagnet. Z2 vortices appear as elementary excitations in the triangular lattice Heisenberg antiferromagnet. Such Z2 vortices are ubiquitous in other frustrated Heisenberg spin systems that have noncollinear long-range orders. In this study, we investigate a possible topological phase transition driven by the binding–unbinding of Z2 vortices. By extracting important degrees of freedom, we map a frustrated spin system to an effective RP3 model. From large-scale Monte Carlo simulation, we obtain an order parameter and a correlation length of up to L = 16384. Concerning the existence of a Z2-vortex transition, by extrapolating the order parameter to the thermodynamics limit assuming the Z2-vortex transition, we obtain a finite transition temperature as \(T_{v}/\tilde{J} \simeq 0.25\). Our estimate of the correlation length at Tv is much larger than L = 16384, which is beyond the previous estimate obtained with the triangular lattice Heisenberg model.