Exact Dynamical Structure Factor of the Degenerate Haldane-Shastry Model

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