Fateev-Zamolodchikov spin chain: excitation spectrum, completeness and thermodynamics

TL;DR

This paper investigates the excitation spectrum, completeness, and thermodynamics of the Fateev-Zamolodchikov spin chain, revealing new solutions and calculating the central charge for different magnetic configurations.

Contribution

It introduces conjectures on Bethe ansatz solutions including exceptional multiplets and non-physical solutions, and computes the central charge for FM and AFM cases.

Findings

Identified physical solutions for the Bethe ansatz equations.

Established completeness and gapless excitation spectrum.

Calculated central charge as c=2(N-1)/(N+2) for FM and c=1 for AFM.

Abstract

The sector of zero $Z_{N}$-charge is studied for the ferromagnetic (FM) and antiferromagnetic (AFM) version of the $Z_{N}\times Z_{2}$ invariant Fateev-Zamolodchikov quantum spin chain. We conjecture that the relevant Bethe ansatz equations should admit, beside the usual string-like solutions, exceptional multiplets, and a number of non-physical solutions. Once the physical ones are identified, we show how to get completeness and the gapless excitation spectrum. The central charge is computed from the specific heat and found to be $c=2\frac{N-1}{N+2}$ (FM) and $c=1$ (AFM).