ANYON REPRESENTATION OF THE GROUND-STATE DEGENERACY OF THE QUANTUM FRUSTRATED XY MODEL

We use the extension of the Jordan-Wigner transformation to planar systems to investigate the quantum frustrated XY model for spin 1/2 on a square lattice. We find that this model is mapped into the hopping Hamiltonian for a planar spinless electron in a transverse magnetic field. When we fix the frustration parameter to be a rational number such that the electron density is proportional to the total flux threading the plaquette, the model is equivalent to a Z(N) gauge theory of anyons. The Z(N) symmetry of the anyon theory implies a degeneracy 2N for the ground state of the model considered. Since we regard the frustration field as classical background, our approach has to be considered as a mean-field theory of the frustrated spin model. We briefly discuss the effect of quantum corrections to the ground-state degeneracy.