Particle-hole symmetry of the fractional quantum Hall effect in the lowest Landau level

Electrons confined to two-dimensions experience the fractional quantum Hall effect (FQHE) at low electron densities, high magnetic fields, and low temperatures. FQHE states are topologically ordered phases characterized by the electron filling factor ν which is the electron number divided by the Landau level degeneracy. Alternatively, under particle-hole conjugation of a spin-polarized system confined to a single Landau level one can consider the system in terms of holes (the absence of an electron) with a hole filling factor of νh = 1 - ν. Naively, if the system maintains particle-hole symmetry, then the FQHE at filling factor ν will also occur at 1- ν with all the same properties. However, realistic effects such as Landau level mixing can break particle-hole symmetry at the level of the Hamiltonian through the inclusion of three-body terms. We study the nature of particle-hole symmetry on the FQHE in the lowest Landau level under realistic conditions numerically using exact diagonalization.