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 quantum Hall (FQH) systems. This success cannot be attributed to a cancellation be tween 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 f unction of pair angular momentum) in the lowest Landau level (LL). The clas s of short-range repulsive pseudopotentials is defined that lead to short-r ange Laughlin-like correlations in many-body systems and to which the CF mo del can be applied. These Laughlin correlations are described quantitativel y using the formalism of fractional parentage. The discussion is illustrate d with an analysis of the energy spectra obtained in numerical diagonalizat ion of up to 11 electrons in the lowest and excited LLs. The qualitative di fference 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 stat e is not a Laughlin v = 1/3 state in the first excited LL. The analysis of the involved pseudopotentials also explains the success or failure of the C F picture when applied to other systems of charged fermions with Coulomb re pulsion, such as the Laughlin quasiparticles in the FQH hierarchy or charge d excitons in an electron-hole plasma.