EXACT SPECTRUM OF SU(N) SPIN CHAIN WITH INVERSE-SQUARE EXCHANGE

The spectrum and partition function of a nonuniform spin chain with lo ng-range interactions are derived. The model consists of SU(n) spins p ositioned at the equilibrium positions of a classical Calogero model a nd interacting with an external magnetic field and through mutual exch ange terms with strength inversely proportional to the square of their distance. The energy levels are found to be equidistant and to have a high degree of degeneracy, with several SU(n) multiplets grouping int o the same energy eigenspace. The partition function takes the form of a q-deformed polynomial. This leads to a description of the system in terms of an effective parafermionic hamiltonian, and to a classificat ion of the states in terms of ''modules'' consisting of base-n string of integers.