Numerically study the conformality of Q-state 1+1D quantum Potts model at Q>4

The existence of complex conformal field theory (CFT) is proposed to be a mechanism of weak first order phase transition featuring extremely slow renormalization group flow with approximate scale invariance. We numerically study the simplest platform of this physics — the Q-state 2D Potts model when Q>4. We find that the properties of the phase transition are well captured by the complex CFTs. The central charge and conformal tower are extracted and studied. We also analyze how these data rely on length scale using conformal perturbation theory away from the nearby complex CFT.