Quasi-particles in the chiral Potts model

We study the quasi-particle spectrum of the integrable three-state chiral Potts chain in the massive phase by combining a numerical study of the zeroes of associated transfer matrix eigenvalues with the exact results of the ferromagnetic three-state Potts chain and the three-state superintegrable chiral Potts model. We find that the spectrum is described in terms of quasi-particles with momenta restricted only to segments of the Brillouin zone $0\leq P \leq 2\pi$ where the boundaries of the segments depend on the chiral angles of the model.