Coloron excitations of the SU(3) Haldane--Shastry model

TL;DR

This paper rigorously proves the exact wave function for coloron excitations in the SU(3) Haldane--Shastry model, demonstrating fractional statistics and constructing explicit eigenstates, with implications for SU(n) generalizations.

Contribution

It provides an exact construction and proof of coloron wave functions and eigenstates in the SU(3) Haldane--Shastry model, including fractional statistics analysis.

Findings

Colorons are free particles with shifted momentum spacings due to fractional statistics.

Explicit eigenstates for two-coloron systems are constructed.

Results are generalized to SU(n) models.

Abstract

In a recent publication, we proposed two possible wave functions for the elementary excitations of the SU(3) Haldane--Shastry model (HSM), but argued on very general grounds that only one or the other can be a valid excitation. Here we provide the explicit details of our calculation proving that the 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. We further provide an explicit construction of the exact color-polarized two-coloron eigenstates, and thereby show that colorons are free but that their relative momentum spacings are shifted according to fractional statistics with parameter $g=2/3$. We evaluate the SU(3) spin currents. Finally, we interpret our results within the framework of the asymptotic Bethe Ansatz and generalize some of them to the case of SU($n$).