Excitation Spectrum and Correlation Functions of the Z_3-Chiral Potts Quantum Spin Chain

TL;DR

This paper investigates the excitation spectrum and correlation functions of the Z_3-chiral Potts quantum spin chain, revealing a quasiparticle band structure and stable second particles across a range of parameters using perturbation and numerical methods.

Contribution

It provides new insights into the quasiparticle structure and stability of excitations in the Z_3-chiral Potts model, including the superintegrable case, through combined analytical and numerical analysis.

Findings

The excitation spectrum exhibits a quasiparticle band structure.

The second fundamental particle remains stable over a limited momentum range.

Correlation functions show oscillatory behavior related to dispersion properties.

Abstract

We study the excitation spectrum and the correlation functions of the 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.