On the interaction energy of 2D electron FQHE systems within the Chern-Simons approach

The interaction energy of the two-dimensional electron system in the region of fractional quantum Hall effect is considered within the Chern-Simons composite fermion approach. In the limit when Coulomb interaction is very small comparing to the cyclotron energy the RPA results are obtained for the fillings $\nu=1/3, 1/5, 2/3, 2/5, 3/7$ and compared with the exact diagonalization results for small systems (extrapolated for infinite systems). They show very poor agreement suggesting the need for looking for alternative approaches.