Models with inverse-square exchange

A one-dimensional quantum N-body system of either fermions or bosons with SU(n) ''spins'' (or colors in particle physics language) interacting via inverse-square exchange is presented in this paper. A class of eigenstates of both the continuum and lattice version of the model Hamiltonians is constructed in terms of the Jastrow-product-type wave function. The class of states we construct in this paper corresponds to the ground state and the low-energy excitations of the model that can be described by the effective harmonic fluid Hamiltonian. By expanding the energy about the ground state we find the harmonic fluid parameters (i.e., the charge, spin velocities, etc.) explicitly. The correlation exponent and the compressibility are also found. As expected, the general harmonic relation [i.e., vS=(vNvJ)1/2] is satisfied among the charge and spin velocities.