Edge Excitations and Non-Abelian Statistics in the Moore-Read State: A Numerical Study in the Presence of Coulomb Interaction and Edge Confinement

TL;DR

This study numerically investigates the Moore-Read state in fractional quantum Hall systems, revealing stable ground states and edge excitations with non-Abelian quasiholes influenced by Coulomb interaction and confinement.

Contribution

It provides a detailed numerical analysis of the stability and edge excitations of the Moore-Read state considering Coulomb interaction and edge confinement effects.

Findings

Moore-Read ground state is stable in a narrow parameter window

Edge excitations include fermionic and bosonic branches with different velocities

Charge +e/4 quasiholes exhibit non-Abelian statistics due to boundary condition changes

Abstract

We study the ground state and low-energy excitations of fractional quantum Hall systems on a disk at filling fraction $\nu = 5/2$, with Coulomb interaction and background confining potential. We find the Moore-Read ground state is stable within a finite but narrow window in parameter space. The corresponding low-energy excitations contain a fermionic branch and a bosonic branch, with widely different velocities. A short-range repulsive potential can stabilize a charge $+e/4$ quasihole at the center, leading to a different edge excitation spectrum due to the change of boundary conditions for Majorana fermions, clearly indicating the non-Abelian nature of the quasihole.