No abstract

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 article. 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. v S = (v N v J ) 1/2 ) is satisfied among the charge and spin velocities.

One-dimensional (1D) model of non-relativistic particles with inverse-square interaction potential known as Calogero-Sutherland Model (CSM) is shown to possess fractional statistics. Using the theory of Jack symmetric polynomial the exact dynamical density-density correlation function and the one-particle Green's function (hole propagator) at any rational interaction coupling constant λ = p/q are obtained and used to show clear evidences of the fractional statistics. Motifs representing the eigenstates of the model are also constructed and used to reveal the fractional exclusion statistics (in the sense of Haldane's "Generalized Pauli Exclusion Principle"). This model is also endowed with a natural exchange statistics (1D analog of 2D braiding statistics) compatible with the exclusion statistics.