Variational Monte Carlo calculation of the spin gap in the ν=1 quantum Hall liquid

A variational method of calculating the spin 1 excitation energies of the ν=1 quantum Hall liquid is presented in detail. We are able to include Landau-level mixing and finite-thickness effects. The many-body wave functions of the states near ν=1 filling are taken to be a product of a lowest-Landau-level Laughlin-type wave function and a Jastrow factor. A significant reduction in the calculated spin gap is found due both to Landau-level mixing (∼40% at rs=1) and to the effect of the finite thickness of the liquid (a further ∼30% at rs=1). We find our calculations to be consistent with recent photoluminescence experiments in δ-doped samples. copyright 1997 The American Physical Society