Spinons in the Haldane–Shastry model: An ideal gas of half-fermions

Martin Greiter, Dirk Schuricht

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.

H. A. Buchdahl

V. V. Aizenshtadt, V. A. Malyshev

F. D. M. Haldane

Dirk Schuricht

We study the relation of Yangians and spinons in the SU( n ) Haldane–Shastry model. The representation theory of the Yangian is shown to be intimately related to the fractional statistics of the spinons. We construct the spinon Hilbert space from tensor products of the fundamental representations of the Yangian.