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

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($n$).

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• Exact results for SU(3) spin chains: trimer states, valence bond solids, and their parent Hamiltonians
• Quantum spin models for the SU(n)_1 Wess-Zumino-Witten model
• Universal entanglement spectra in critical spin chains
• Many-spinon states and the secret significance of Young tableaux
• Exact models for trimerization and tetramerization in spin chains
• Parent Hamiltonians for lattice Halperin states from free-boson conformal field theories
• Charge excitations in SU(n) spin chains: exact results for the 1/r^2 model
• Many-spinon states and representations of Yangians in the SU(n) Haldane--Shastry model
• Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain
• Momentum classification of SU($n$) spin chains using extended Young Tableaux
• The dynamical structure factor of the SU(3) Heisenberg chain: The variational Monte Carlo approach