Electron operator at the edge of the 1/3 fractional quantum Hall liquid

TL;DR

This paper uses quantum Monte Carlo simulations to analyze edge excitations in the 1/3 fractional quantum Hall state, confirming some theoretical predictions and exploring interaction effects with larger systems.

Contribution

It extends previous work by analyzing larger systems and provides more accurate data on edge excitations, including effects of Coulomb interactions.

Findings

Results agree with chiral Luttinger liquid predictions for short-range interactions.

Extended system size analysis offers deeper insight into thermodynamic limits.

Interaction effects on edge excitations remain inconclusive with Coulomb ground states.

Abstract

This study builds upon the work of Palacios and MacDonald (Phys. Rev. Lett. {\bf 76}, 118 (1996)), wherein they identify the bosonic excitations of Wen's approach for the edge of the 1/3 fractional quantum Hall state with certain operators introduced by Stone. Using a quantum Monte Carlo method, we extend to larger systems containing up to 40 electrons and obtain more accurate thermodynamic limits for various matrix elements for a short range interaction. The results are in agreement with those of Palacios and MacDonald for small systems, but offer further insight into the detailed approach to the thermodynamic limit. For the short range interaction, the results are consistent with the chiral Luttinger liquid predictions.We also study excitations using the Coulomb ground state for up to nine electrons to ascertain the effect of interactions on the results; in this case our tests of the chiral Luttinger liquid approach are inconclusive.