Conformal Field Theory Approach to Abelian and Non-Abelian Quantum Hall Quasielectrons

The quasiparticles in quantum Hall liquids carry fractional charge and obey fractional quantum statistics. Of particular recent interest are those with non-Abelian statistics, since their braiding properties could, in principle, be used for robust coding of quantum information. There is already a good theoretical understanding of quasiholes in both Abelian and non-Abelian quantum Hall states. Here we develop conformal field theory methods that allow for an equally precise description of quasielectrons and explicitly construct two- and four-quasielectron excitations of the non-Abelian Moore-Read state.

Figure 1

Main plot: Excess charge $\Delta q$ of the two MR quasielectrons for $N=16$ particles on the sphere geometry ($\theta$ being the polar angle). The two quasielectrons with charge $e/4$ at $\nu =1/2$ are placed at the antipodes of a sphere corresponding to $\theta =0$ and $\theta =\pi$. The calculation has been done using Monte Carlo integration. Inset: Corresponding density profile.