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

Abstract

:We study the excitation spectrum and the correlation functions of the Z Z 3 -chiral Potts model in the massive high-temperature phase using perturbation expansions and numerical diagonalization. We are mainly interested in results for general chiral angles but we consider also the superintegrable case. For the parameter values considered, we find that the band structure of the low-lying part of the excitation spectrum has the form expected from a quasiparticle picture with two fundamental particles.Studying the N-dependence of the spectrum, we confirm the stability of the second fundamental particle in a limited range of the momentum, even when its energy becomes so high that it lies very high up among the multiparticle scattering states. This is not a phenomenon restricted to the superintegrable line.Calculating a non-translationally invariant correlation function, we give evidence that it is oscillating. Within our numerical accuracy we find a relation between the oscillation length and the dip position of the momentum dispersion of the lightest particle which seems to be quite independent of the chiral angles.

Spontaneous magnetization of the integrable chiral Potts model

“…Several partial results on the pair correlations in the superintegrable quantum spin chain already exist, including some results for the leading asymptotic long separation behavior from finite-size calculations and conformal field theory [24,25], a few terms in series expansions in the coupling constant [26][27][28][29][30], results using the density matrix renormalization group technique [31] and a few exact results for very small chains [32]. Using exact knowledge of the eigenvectors much more can be done for the superintegrable spin chain, but in this paper we rather go in the vertical direction in figure 1, as this will allow us to describe what is needed for the more general integrable chiral Potts model and to express the order parameters in terms of inner products of ground state vectors.…”