Low-temperature expansions and correlation functions of the Z₃-chiral Potts model

Using perturbative methods we derive new results for the spectrum and correlation functions of the general Z₃-chiral Potts quantum chain in the massive low-temperature phase. Explicit calculations of the ground-state energy and the first excitations in the zero momentum sector give excellent approximations and confirm the general statement that the spectrum in the low-temperature phase of general Z_n-spin quantum chains is identical to one in the high-temperature phase where the role of charge and boundary conditions are interchanged. Using a perturbative expansion of the ground state for the Z₃ model we are able to gain some insight into correlation functions. We argue that they might be oscillating and give estimates for the oscillation length as well as the correlation length.