Interacting particles as neither bosons nor fermions: A microscopic origin for fractional exclusion statistics

We study a quantum liquid of particles interacting via a long-ranged two-body potential in three dimensions where the original particles are supposed to be either bosons or fermions. We show that such liquids exhibit the nature of a quantum liquid with fractional exclusion statistics. In both quantum liquids enlarged pseudo-Fermi surfaces are formed from bosons and fermions, although with different excitations. Hence, we conclude that the microscopic origin of exclusion statistics comes from the nature of long-ranged two-body interactions between the particles.