Multi-particle structure in the Z_n-chiral Potts models

The authors calculate the lowest translationally invariant levels of the Z₃- and Z₄-symmetrical chiral Potts quantum chains, using numerical diagonalization of the Hamiltonian for N<or=12 and N<or=10 sites, respectively, and extrapolating n to infinity . In the high-temperature massive phase they find that the pattern of the low-lying zero momentum levels can be explained assuming the existence of n-1 particles carrying Z_n charges Q=1, . . ., n-1 (mass m_Q), and their scattering states. In the superintegrable case the masses of the n-1 particles become proportional to their respective charges: m_Q=Qm₁. Exponential convergence in N is observed for the single-particle gaps, while power convergence is seen for the scattering levels. They also verify that qualitatively the same pattern appears for the self-dual and integrable cases. For general Z_n they show that the energy-momentum relations of the particles show a parity nonconservation asymmetry which for very high temperatures is exclusive due to the presence of a macroscopic momentum P_m=(1-2Q/n) phi , where phi is the chiral angle and Q is the Z_n charge of the respective particle.