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

This study builds upon the work of Palacios and MacDonald [Phys. Rev. Lett. 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 this approach 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 a detailed approach to the thermodynamic limit. For the short range interaction, the results are consistent with 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.