Critical excitation spectrum of a quantum chain with a local three-spin coupling

Using the phenomenological renormalization group (PRG), we evaluate the low-energy excitation spectrum along the critical line of a quantum spin chain having a local interaction between three Ising spins and longitudinal and transverse magnetic fields, i.e., a Turban model. The low-energy excitation spectrum found with the PRG agrees with the spectrum predicted for the (D(4),A(4)) conformal minimal model under a nontrivial correspondence between translations at the critical line and discrete lattice translations. Under this correspondence, the measurements confirm a prediction that the critical line of this quantum spin chain and the critical point of the two-dimensional three-state Potts model are in the same universality class.