New exact analytical results for two quasiparticle excitation in the fractional quantum Hall effect

In this work, two quasiparticle excitation energies per particle are calculated analytically for systems with up to $N = 7$ electrons in both Laughlin and composite fermions (CF) theories by considering the full jellium potential which consists of three parts, the electron-electron, electron-background, and background-background Coulomb interactions. The exact results we have obtained confirm the fact that the CF-wavefunction for two quasiparticles has lower energy than Laughlin wavefunction though the found difference between Laughlin and (CF) two quasiparticle energies decreases as the system size increases.