Theoretical estimates for the correlation energy of the unprojected composite fermion wave function

The most prominent filling factors of the fractional quantum Hall effect are very well described by the Jainʹs microscopic composite fermion wave function. Through these wave functions, the composite fermion theory recovers the Laughlinʹs wave function as a special case and exposes itself to rigorous tests. Considering the system as being in the thermodynamic limit and using simple arguments, we give theoretical estimates for the correlation energy corresponding to all unprojected composite fermion wave functions in terms of the accurately known correlation energies of the Laughlinʹs wave function. The provided theoretical estimates are in very good agreement with available Monte Carlo data extrapolated to the thermodynamic limit. These results can be quite instructive to test the reliability and accuracy of different computational methods employed on the study of these phenomena.