Asymptotic Bethe-ansatz solution of multicomponent quantum systems with1r2long-range interaction

Asymptotic Bethe-ansatz solutions are obtained for one-dimensional quantum systems with a $\frac{1}{r^2}$ long-range interaction by generalizing Sutherland's method to multicomponent quantum systems. We obtain the solutions to the supersymmetric $t-J$ model of Kuramoto and Yokoyama, the $\mathrm{SU}\left(\nu \right)$ Haldane-Shastry model, and the multicomponent $t-J$ model. The excitation spectrum as well as bulk quantities are computed analytically. Conformal properties of low-energy excitations are discussed in connection with Luttinger liquid theory.