No attraction between spinons in the Haldane-Shastry model

While the Bethe ansatz solution of the Haldane-Shastry model appears to suggest that the spinons represent a free gas of half-fermions Bernevig, Giuliano, and Laughlin (BGL) [Phys. Rev. Lett. 86, 3392 (2001); Phys. Rev. B 64, 24425 (2001)] have concluded recently that there is an attractive interaction between spinons. We argue that the dressed scattering matrix obtained with the asymptotic Bethe ansatz is to be interpreted as the true and physical scattering matrix of the excitations, and hence, that the result by BGL is inconsistent with an earlier result by Essler [Phys. Rev. B 51, 13357 (1995)]. We critically reexamine the analysis of BGL, and conclude that there is no interaction between spinons or spinons and holons in the Haldane-Shastry model.