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

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

2005-11-24

arxiv.org/abs/cond-mat/0511604v2

Phys. Rev. B 73, 235105 (2006).

Physics

Condensed Matter

Strongly Correlated Electrons

Scientific paper

10.1103/PhysRevB.73.235105

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($n$).

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