Conformal field theory and edge excitations for the principal series of quantum Hall fluids

TL;DR

This paper proposes a modified edge theory for fractional quantum Hall states at specific filling factors, introducing twist fields to better match experimental observations and alter neutral mode charges.

Contribution

It introduces a novel approach using twist fields in the edge theory to account for flux quanta effects in fractional quantum Hall states.

Findings

Green function decay exponent varies continuously with filling factor

Neutral mode charges are effectively removed by the twist fields

The modified theory aligns better with recent experimental results

Abstract

Motivated by recent experimental results, we reconsider the theory of the edge excitations for the fractional Hall effect at filling factors $\nu=p/(2np+1)$. We propose to modify the standard $u(1)\otimes su(p)$ edge theory for this series by introducing twist fields which change the boundary conditions of the bosonic fields and simulate the effect of fractions of flux quanta $\phi_0/p$. This has the effect of removing the conserved charges associated to the neutral modes while keeping the right statistics of the particles. The Green function of the electron in presence of twists decays at long distance with an exponent varying continuously with $\nu$.