"Quasielectrons in Lattice Moore–Read Models"

Anyons are fractionally charged quasiparticles which are neither fermions nor bosons. Anyons exhibit fractional statistics and important for topological quantum computation. Anyonic Moore–Read states provides a well explored description for the insertion of quasiholes in the continuum. However, quasielectron insertion creates a singularity in the continuum state which further complicates the problem. In this work we show that the singularity problem can be avoided by placing quasielectrons in fractional quantum Hall lattice systems. We construct Moore–Read Pfaffian states for filling fraction 5/2 and incorporate quasiholes and quasielectrons. We investigate density profile, charge, size and braiding properties of the anyons by means of a Metropolis Monte Carlo simulation. Further we derive a few body parent Hamiltonian for the states. Additionally we investigate density profile, charge and shape of the anyons in the Kapit–Mueller model by employing an exact diagonalization technique. We compare our results for the analytical states with the anyons in the Kapit–Mueller model.