Landau Level Mixing in the Perturbative Limit

We study the effects of Landau level mixing in the limit of weak electron interaction. We use a numerical method to obtain the two- and three-body corrections to quantum Hall pseudopotentials, which are exact to lowest order in the Landau level mixing parameter. Our results are in general agreement with certain analytic results (some derived here, some derived by other authors) in the thermodynamic limit. We find that the convergence to this thermodynamic limit can be slow. This suggests that errors could occur if one tries to use pseudopotentials derived in a thermodynamic limit for numerical work on finite systems.