SU(ν) Generalization of Twisted Haldane-Shastry Model

Abstract

The SU($ν$) generalized Haldane-Shastry spin chain with $1/r^2$ interaction is studied with twisted boundary conditions. The exact wavefunctions of Jastrow type are obtained for every rational value of the twist angle in unit of $2π$. The spectral flow of the ground state is then discussed as a function of the twist angle. By resorting to the motif picture in the Bethe ansatz method, we show that the period of the spectral flow is $ν$, which is determined by the statistical interaction in exclusion statistics.