Complementary colors of colorons: the elementary excitations of the SU(3) Haldane--Shastry model

TL;DR

This paper introduces and proves the exact form of a specific elementary excitation called a coloron in the SU(3) Haldane--Shastry model, analyzing its properties and generalizing to SU(n).

Contribution

It provides a rigorous proof of the exact wave function for a coloron excitation and explores its dispersion and statistics, extending the understanding of SU(3) spin chains.

Findings

Exact wave function for a coloron excitation is derived.

Dispersion relation and exclusion statistics of colorons are obtained.

Results are compared with the asymptotic Bethe Ansatz and generalized to SU(n).

Abstract

We propose two possible trial wave functions for the elementary excitations of the SU(3) Haldane--Shastry model, but then argue on very general grounds that only one or the other can be a valid excitation. We then prove explicitly that the trial wave function describing a coloron excitation which transforms according to representation $\bar{3}$ under SU(3) rotations if the spins of the original model transform according to representation 3, is exact. If a basis for the spins on the chain is spanned by the colors blue, red, and green, a basis for the coloron excitations is hence given by the complementary colors yellow, cyan, and magenta. We obtain the dispersion and the exclusion statistics among polarized colorons. Furthermore, we compare our results with the asymptotic Bethe Ansatz and discuss the generalization to SU($n$).