Fractional quantum Hall effect at $\nu = 5/2$: Ground states, non-Abelian quasiholes, and edge modes in a microscopic model

TL;DR

This paper numerically investigates the $ u=5/2$ fractional quantum Hall system, analyzing ground states, quasiholes, and edge modes, and explores conditions favoring Moore-Read and anti-Pfaffian states with implications for non-Abelian quasiparticle detection.

Contribution

It provides a detailed phase diagram and analysis of edge mode velocities, quasihole excitations, and the conditions favoring Moore-Read or anti-Pfaffian states in a microscopic model.

Findings

Separation of charge and neutral edge mode velocities causes decoherence.

Estimated decoherence length is around four microns.

Weak confinement favors anti-Pfaffian, strong confinement favors Moore-Read.

Abstract

We present a comprehensive numerical study of a microscopic model of the fractional quantum Hall system at filling fraction $\nu = 5/2$, based on the disc geometry. Our model includes Coulomb interaction and a semi-realistic confining potential. We also mix in some three-body interaction in some cases to help elucidate the physics. We obtain a phase diagram, discuss the conditions under which the ground state can be described by the Moore-Read state, and study its competition with neighboring stripe phases. We also study quasihole excitations and edge excitations in the Moore-Read--like state. From the evolution of edge spectrum, we obtain the velocities of the charge and neutral edge modes, which turn out to be very different. This separation of velocities is a source of decoherence for a non-Abelian quasihole/quasiparticle (with charge $\pm e/4$) when propagating at the edge; using numbers obtained from a specific set of parameters we estimate the decoherence length to be around four microns. This sets an upper bound for the separation of the two point contacts in a double point contact interferometer, designed to detect the non-Abelian nature of such quasiparticles. We also find a state that is a potential candidate for the recently proposed anti-Pfaffian state. We find the speculated anti-Pfaffian state is favored in weak confinement (smooth edge) while the Moore-Read Pfaffian state is favored in strong confinement (sharp edge).