Composite fermions and quantum Hall systems: Role of the Coulomb pseudopotential

The mean-field composite fermion (CF) picture successfully predicts angular momenta of multiplets forming the lowest-energy band in fractional auantum Hall (FQH) systems. This success cannot be attributed to a cancellation between Coulomb and Chern-Simons interactions beyond the mean field, because these interactions have totally different energy scales. Rather, it results from the behaviour of the Coulomb pseudopotential V(L) (pair energy as a function of pair angular momentum) in the lowest Landau level (LL). The class of short-range repulsive pseudopotentials is defined that lead to short-range Laughlin-like correlations in many-body systems and to which the CF model can be applied. These Laughlin correlations are described quantitatively using the formalism of fractional parentage. The discussion is illustrated with an analysis of the energy spectra obtained in numerical diagonalization of up to 11 electrons in the lowest and excited LLs. The qualitative difference in the behaviour of V(L)is shown to invalidate sometimes the mean-field CF picture when applied to higher LLs. For example, the v =(7/3)state is not a Laughlin v =⅓state in the first excited LL. The analysis of the involved pseudopotentials also explains the success or failure of the CF picture when applied to other systems of charged fermions with Coulomb repulsion, such as the Laughlin auasiparticles in the FQH hierarchy or charged excitons in an electron-hole plasma.