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

Abstract

Using perturbative methods we derive new results for the spectrum and correlation functions of the general Z Z 3 -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 Z n -spin quantum chains is identical to one in the high-temperature phase where the rôle of charge and boundary conditions are interchanged. Using a perturbative expansion of the ground state for the Z Z 3 model we are able to gain some insight in correlation functions. We argue that they might be oscillating and give estimates for the oscillation length as well as the correlation length.

Analyticity and integrability in the chiral Potts model

“…In the case of N = 3 there have been previous perturbation studies both for small [13]- [14] and large [14]- [16] k and Table 1 agrees with the small k results of [14] which were obtained to order 7. Many of the details of the perturbation expansion are discussed in these papers.…”

Quasi-Particles in the Chiral Potts Model

“…We conclude in sec. 4 by using this study to connect the two exact spectra together, and we contrast our study with previous results [19]- [21]. Our principle conclusions are that 1) there is a sense in which the superintegrable spectrum is more properly regarded as consisting of three rather than two quasi-particles 2) the momentum ranges for these three types of quasi-particle are different and 3) as we move smoothly from the superintegrable to the ferromagnetic three-state Potts point the allowed momentum range of two of the quasiparticles shrinks to zero while the range of the third expands to fill the entire Brillouin zone.…”

“…This problem is seen vividly if we compare our conjecture of sec. 2 with the numerical studies and interpretation of [19] [21]. In these studies the spectrum of the massless ferromagnetic three-state Potts model is interpreted as a quasi-particle spectrum made up of two excitations .…”

“…However there is an identity on q-series [34] which makes these two different looking fermionic forms of the character equal. If the study of [19]- [21] is a correct interpretation of the numerical data then this identity of characters must have an extension to the order one spectrum. Let us assume such an identity and examine its consequences.…”

Excitation spectrum and correlation functions of theZ3 chiral Potts quantum spin chain

“…In this paper we have presented further numerical evidence that the spectrum of the general Z Z 3 -spin quantum chain (1) in the massive high-temperature phase can be interpreted in terms of two fundamental quasiparticles and their scattering states. Using duality [11] our results about the quasiparticle spectra can be pulled over to the massive low-temperature phase.…”