Is there an attraction between spinons in the Haldane--Shastry model?

TL;DR

This paper investigates whether spinons in the Haldane--Shastry model attract or behave as free particles, concluding that they are non-interacting based on a critical analysis of previous scattering matrix interpretations.

Contribution

The paper clarifies the nature of spinon interactions in the Haldane--Shastry model, arguing against previous claims of attraction by analyzing the physical scattering matrix.

Findings

Spinons do not attract in the Haldane--Shastry model.

The dressed scattering matrix reflects true excitations.

Previous claims of attraction are inconsistent with earlier results.

Abstract

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) (cond-mat/0011069, cond-mat/0011270) 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 (cond-mat/9406081). We critically re-examine the analysis of BGL, and conclude that there is no interaction between spinons or spinons and holons in the Haldane--Shastry model.