Exact solution and spectral flow for twisted Haldane-Shastry model

The exact solution of the spin chain model with $1/r^2$ exchange is found for twisted boundary conditions. The spectrum thus obtained can be reproduced by the asymptotic Bethe ansatz. The spectral flow of each eigenstate is determined exactly as a function of the twist angle. We find that the period $4\pi$ for the ground state nicely fits in with the notion of fractional exclusion statistics.