Monte Carlo Comparison of Quasielectron Wave Functions

TL;DR

This paper compares different variational wave functions for quasielectron excitations in the fractional quantum Hall effect using Monte Carlo methods, finding similar results for Coulomb interactions but slight differences in energy gaps.

Contribution

It provides a Monte Carlo comparison of Laughlin and Jain composite fermion wave functions for quasielectrons at various filling fractions.

Findings

Results for both wave functions are similar for Coulomb interactions.

Composite fermion wave function yields slightly smaller energy gaps.

Energy gaps are closer to exact diagonalization results.

Abstract

Variational Monte Carlo calculations of the quasielectron and quasihole excitation energies in the fractional quantum Hall effect have been carried out at filling fractions $\nu=1/3$, 1/5, and 1/7. For the quasielectron both the trial wave function originally proposed by Laughlin and the composite fermion wave function proposed by Jain have been used. We find that for long-range Coulomb interactions the results obtained using these two wave functions are essentially the same, though the energy gap obtained using the composite fermion quasielectron is slightly smaller, and closer to extrapolated exact-diagonalization results.