Mutual Exclusion Statistics Between Quasiparticles in the F ractional Quantum Hall Effect

In this paper, we propose a new assignment for mutual exclusion statistics between quasielectrons and quasiholes in the fractional quantum Hall effect. To support this assignment, we provide numerical evidence and demonstrate that the physical origin of this mutual statistics stems from a novel hard-core constraint, arising due to correlations between the distinguishable vortex-like quasiparticles. Our investigation reveals that a two-dimensional electron system in a strong magnetic field exhibits the fractional quantum Hall effect (FQHE) at specific 'magic' fillings, such as ν = 1/m, where m is an odd integer. We focus on the exotic quantum numbers associated with the quasiparticles, particularly how the exchange of quasiholes or quasielectrons leads to their wave functions acquiring fractional phases. Additionally, we develop a unique counting rule that governs the statistical behavior of these quasiparticles, allowing us to uncover linear dependencies and the corresponding statistical exclusion conditions. Our findings contribute to the understanding of the underlying physics of the FQHE and the intricate behavior of its quasiparticles.