A Systematic Method for Constructing Realistic Potentials in Real Space for Use in Fractional Quantum Hall Monte Carlo Simulations

Abstract

We develop a method for efficiently generating real space potentials which incorporate realistic effects into Monte Carlo calculations of fractional quantum Hall energy gaps. We apply the method to the effect Landau level mixing, which creates a discrepancy between experimental measurements and theoretical predictions in graphene. We fit perturbative, two-body, Landau level mixing-incorporated Haldane pseudopotential corrections to data in the lowest Landau level. We develop an effective real space potential V_eƒƒ(r,κ,Q) which maps to corrected pseudopotentials on the Haldane sphere for Landau level mixing parameter κ and magnetic monopole strength Q. We use this effective potential to calculate Landau level mixing-incorporated energy gaps for fractional quantum Hall states of graphene via the Metropolis-Hastings Monte Carlo algorithm and benchmark the results against exact diagonalization. We find that the Metropolis Hastings algorithm does not sample the more dense electron configurations most affected by Landau level mixing and suggest further study developing an algorithm that will sample them.