Entanglement entropy and massless phase in the antiferromagnetic three-state quantum chiral clock model

The von Neumann entanglement entropy is used to estimate the critical point hc/J≃0.143(3) of the mixed ferro-antiferromagnetic three-state quantum Potts model H=i[J(XiXi+12+Xi2Xi+1)-hRi], where Xi and Ri are standard three-state Potts spin operators and J>0 is the antiferromagnetic coupling parameter. This critical point value gives improved estimates for two Kosterlitz-Thouless transition points in the antiferromagnetic (β<0) region of the Δ-β phase diagram of the three-state quantum chiral clock model, where Δ and β are, respectively, the chirality and coupling parameters in the clock model. These are the transition points βc≃-0.143(3) at Δ=12 between incommensurate and commensurate phases and βc≃-7.0(1) at Δ=0 between disordered and incommensurate phases. The von Neumann entropy is also used to calculate the central charge c of the underlying conformal field theory in the massless phase h≤hc. The estimate c≃1 in this phase is consistent with the known exact value at the particular point h/J=-1 corresponding to the purely antiferromagnetic three-state quantum Potts model. The algebraic decay of the Potts spin-spin correlation in the massless phase is used to estimate the continuously varying critical exponent η.