Exact dynamical structure factor of the degenerate Haldane-Shastry model

TL;DR

This paper derives the exact dynamical structure factor for the K-component Haldane-Shastry model at zero temperature, revealing a free quasi-particle interpretation and singularities at spectral edges, with numerical validation.

Contribution

It provides the first exact analytical expression for the dynamical structure factor of the K-component Haldane-Shastry model, generalizing the spinon picture.

Findings

Exact expression for $S(q,)$ derived

Divergent singularities at spectral edges analytically obtained

Numerical checks confirm analytical results

Abstract

The dynamical structure factor $S(q,\omega)$ of the K-component (K = 2,3,4) spin chain with the 1/r^2 exchange is derived exactly at zero temperature for arbitrary size of the system. The result is interpreted in terms of a free quasi-particle picture which is generalization of the spinon picture in the SU(2) case; the excited states consist of K quasi-particles each of which is characterized by a set of K-1 quantum numbers. Divergent singularities of $S(q,\omega)$ at the spectral edges are derived analytically. The analytic result is checked numerically for finite systems.