Quantum mechanics of the fractional-statistics gas: Hartree-Fock approximation

Abstract

The two-dimensional ideal gas of particles obeying ν fractional statistics is transformed to the Fermi representation and studied in the Hartree-Fock approximation. The extremal ground state is shown to be composed of Landau orbitals. When the filling factor (1-ν${)}^{\mathrm{-}1}$ of the ground state is an integer, a logarithmically large energy gap appears in the single-particle excitation spectrum, and the particle and hole states are charged vortices with circulation ±(1-ν)h/m. The linear dependence of the total energy on the density, together with the presence of this gap, suggests that the true ground state at these fractions is a superfluid.