The mean field composite Fermion (CF) picture successfully predicts angularmomenta of multiplets forming the lowest energy band in fractional quantum Hall(FQH) systems. This success cannot be attributed to a cancellation betweenCoulomb and Chern-Simons interactions beyond the mean field, because theseinteractions have totally different energy scales. Rather, it results from thebehavior of the Coulomb pseudopotential V(L) (pair energy as a function of pairangular momentum) in the lowest Landau level (LL). The class of short rangerepulsive pseudopotentials is defined that lead to short range Laughlin likecorrelations in many body systems and to which the CF model can be applied.These Laughlin correlations are described quantitatively using the formalism offractional parentage. The discussion is illustrated with an analysis of theenergy spectra obtained in numerical diagonalization of up to eleven electronsin the lowest and excited LL's. The qualitative difference in the behavior ofV(L) is shown to sometimes invalidate the mean field CF picture when applied tohigher LL's. For example, the nu=7/3 state is not a Laughlin nu=1/3 state inthe first excited LL. The analysis of the involved pseudopotentials alsoexplains the success or failure of the CF picture when applied to other systemsof charged Fermions with Coulomb repulsion, such as the Laughlin quasiparticlesin the FQH hierarchy or charged excitons in an electron-hole plasma.
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