The Schwinger Model with Perfect Staggered Fermions

We construct and test a quasi-perfect lattice action for staggered fermions. The construction starts from free fermions, where we suggest a new blocking scheme, which leads to excellent locality of the perfect action. An adequate truncation preserves a high quality of the free action. An Abelian gauge field is inserted in d = 2 by effectively tuning the couplings to a few short-ranged lattice paths, based on the behavior of topological zero modes. We simulate the Schwinger model with this action, applying a new variant of Hybrid Monte Carlo, which damps the computational overhead due to the non-standard couplings. We obtain a tiny “pion” mass down to very small β, while the “η” mass follows very closely the prediction of asymptotic scaling. The observation that even short-ranged quasi-perfect actions can yield strong improvement is most relevant in view of QCD.