Dynamical correlations and quantum phase transition in the quantum Potts model

We present a detailed study of the finite-temperature dynamical properties of the quantum Potts model in one dimension. Quasiparticle excitations in this model have internal quantum numbers, and their scattering matrix deep in the gapped phases is shown to take a simple exchange form in the perturbative regimes. The finite-temperature correlation functions in the quantum critical regime are determined using conformal invariance, while far from the quantum critical point we compute the decay functions analytically within a semiclassical approach of Sachdev and Damle [Phys. Rev. B 57, 8307 (1998)]. As a consequence, decay functions exhibit a diffusive character. We also provide robust arguments that our semiclassical analysis carries over to very low temperatures even in the vicinity of the quantum phase transition. Our results are also relevant for quantum rotor models, antiferromagnetic chains, and some spin ladder systems.