Truncated Calogero-Sutherland models on a circle

We investigate a quantum many-body system with particles moving in a circle and subject to two-body and three-body potentials. This class of models, in which the range of interaction r can be set to a certain number of neighbors, extrapolates from a system with interactions up to next-to-nearest neighbors and the celebrated Calogero-Sutherland model. The exact ground state energy and a part of the excitation spectrum have been obtained.