CFT description of the fully frustrated XY model and phase diagram analysis

Following an earlier suggestion, we show how the U(1) ⊗ Z2 symmetry of the fully frustrated XY (FFXY ) model on a square lattice can be accounted for in the framework of the m-reduction procedure developed for a Quantum Hall system at ‘paired states’ fillings ν = 1. The resulting twisted conformal field theory (CFT) with central charge c = 2 is shown to well describe the physical properties of the FFXY model. In particular, the whole phase diagram is recovered by analysing the flow from the Z2 degenerate vacuum of the c = 2 CFT to the infrared fixed point unique vacuum of the c = 3/2 CFT. The last theory is known to successfully describe the critical behaviour of the system at the overlap temperature for the Ising and vortex-unbinding transitions.