In fractional quantum Hall fluids, the quasiparticle excitations are anyons with fractional charges and statistics. Effective interactions among the anyons can be induced by either model or realistic electron-electron (e-e) interactions. Without losing the generality, we investigate such phenomena for the Laughlin $1/3$ and Moore-Read (MR) non-Abelian phases. Anyons display rich internal dynamics in both cases that will lead to interesting experimental consequences. In particular, bound states of two Laughlin anyons are preferred under short-range e-e interactions, leading to $2e/3$—instead of $e/3$—effective charge carriers at low temperatures, which have been seen in several experiments. MR phases host two topologically distinct fusion channels: “1” and “$\psi$.” The different effective interactions of $e/4$ anyons in the two sectors suggest the vanishing of the degeneracy of fusion channels when the e-e interaction is no longer its model Hamiltonian, in which case different bound states could also appear. This indicates the possibility of energetically manipulating the two types of anyons by tuning the bare e-e interactions. We point out that the results of recently developed high-resolution scanning tunneling microscopy measurements will be affected by the effective anyon interactions, where anyons are clustered together after the tunneling of electrons. The low-lying parts of the local density of states affected by various anyon clusters are simulated for both Abelian and non-Abelian systems with (screened) Coulomb interactions.

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• Two-dimensional electron gas
• Exact diagonalization
• Monte Carlo methods
• Scanning tunneling spectroscopy