SPECTRUM OF A SPIN CHAIN WITH INVERSE-SQUARE EXCHANGE

The spectrum of a one-dimensional chain of SU(n) spins positioned at the static equilibrium positions of the particles in the corresponding classical Calogero system with an exchange interaction inversely proportional to the square of their distance is studied. As in the translationally invariant Haldane-Shastry model the spectrum is found to exhibit a very simple structure containing highly degenerate 'super-multiplets'. The algebra underlying this structure is identified and several sets of raising and lowering operators am given explicitly. On the basis of this algebra and numerical studies we give the complete spectrum and thermodynamics of the SU(2) system.