Hartree-Fock ground-state energy of anyons with no Coulomb interaction in the zero effective field

TL;DR

This paper calculates the Hartree-Fock ground-state energy of anyons without Coulomb interaction under a specific magnetic field condition, revealing that certain statistical transmutations are energetically unfavorable at specific filling fractions.

Contribution

It provides a novel Hartree-Fock analysis of anyons in a zero effective field, clarifying their energy landscape and statistical behavior at fractional quantum Hall filling fractions.

Findings

Transmutations to superfermions are not energetically favorable at ν=1/2p.

Ground-state energy is computed for anyons with no Coulomb interaction.

External magnetic field cancels the statistical field in the model.

Abstract

We find, in the Hartree-Fock approximation, the ground-state energy of anyons with no Coulomb interaction in the case when the external magnetic field precisely cancels the average statistical field. From the point of view of the fractional quantum Hall effect statistics transmutations to {\it superfermions} at filling fractions $\nu =1/2p$ are not energetically favourable.