A perturbative approach to spectrum and correlation functions of the chiral Potts model

Abstract

The massive high-temperature phase of the chiral Potts quantum chain is studied using perturbative methods. For the ℤ3-chain we present high-temperature expansions for the ground-state energy and the dispersion relations of the two single-particle states as well as two-particle states at general values of the parameters. We also present a perturbative argument showing that a large class of massive ℤn-spin quantum chains have quasiparticle spectra withn-1 fundamental particles. It is known from earlier investigations that—at special values of the parameters—some of the fundamental particles exist only for limited ranges of the momentum. In these regimes our argument is not rigorous, as one can conclude from a discussion of the radius of convergence of the perturbation series. We also derive correlation functions from a perturbative evaluation of the ground-state for the ℤ3-chain. In addition to an exponential decay we observe an oscillating contribution. The oscillation length seems to be related to the asymmetry of the dispersion relations. We show that this relation is exact at special values of the parameters for general ℤn using a form factor expansion.