Physics beyond quasi-particles: Spectrum and completeness of the 3 state superintegrable chiral Potts model

TL;DR

This paper derives the complete energy spectrum of the 3-state superintegrable chiral Potts model, revealing non-quasi-particle excitations and comparing them with BCS superconductivity and the $S=1$ XXZ spin chain.

Contribution

It establishes the counting rules for energy levels and demonstrates their completeness, providing a full spectrum analysis including non-quasi-particle excitations.

Findings

Complete spectrum of excitations derived in the thermodynamic limit.

Identification of excitations lacking a quasi-particle description.

Comparison with BCS spectrum and $S=1$ XXZ spin chain.

Abstract

We find the rules which count the energy levels of the 3 state superintegrable chiral Potts model and demonstrate that these rules are complete. We then derive the complete spectrum of excitations in the thermodynamic limit in the massive phase and demonstrate the existence of excitations which do not have a quasi-particle form. The physics of these excitations is compared with the BCS superconductivity spectrum and the counting rules are compared with the closely related $S=1$ XXZ spin chain.