Quantum Mechanics of the Fractional-Statistics Gas: Particle-Hole Interaction

We compute the collective-mode spectrum of the fractional-statistics gas using the set of single particle-hole pairs of the Hartree-Fock ground state as a variational basis. We find that the particle-hole interaction reduces the energy of this mode to a finite value but does not cause it to disperse linearly to zero at long wavelengths, as would be expected of a superfluid. We attribute this to a flaw in the variational ground state, implicitly rectified by computing the response functions in the random-phase approximation. The formalism introduced in this paper provides the machinery for performing precise versions of such calculations.