Charge excitations in $\mathrm{SU}\left(n\right)$ spin chains: Exact results for the $1∕r^2$ model

We study the one- and two-holon excitations of the SU(3) Kuramoto-Yokoyama model on the level of explicit wave functions, and generalize the calculations to the case of $\mathrm{SU}\left(n\right)$. We obtain the exact energies and the single-holon momenta, which we find fractionally spaced according to fractional statistics with statistical parameter $g=1∕n$.

Figure 1

$\mathrm{SU}\left(n\right)$ holon dispersion. (a) $n$ even. The allowed momenta fill the interval $[-\frac{\pi }{n},\frac{\pi }{n}]$ for $M$ odd and $[\pi -\frac{\pi }{n},\pi +\frac{\pi }{n}]$ for $M$ even. (b) $n$ odd. The allowed momenta fill the interval $[\pi -\frac{\pi }{n},\pi +\frac{\pi }{n}]$.