Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level

Understand

It is well known that there is a particle-hole symmetry for spin-polarized electrons with two-body interactions in a partially filled Landau level, which becomes exact in the limit where the cyclotron energy is large compared to the interaction strength, so one can ignore mixing between Landau levels.

• This symmetry is explicit in the description of a half-filled Landau level recently introduced by D.
• T.
• Son, using Dirac fermions, but it was thought to be absent in the older fermion-Chern- Simons approach, developed by Halperin, Lee, and Read and subsequent authors.