Optimizing Chirality and Scaling of Lattice Fermion

Abstract

If we construct a lattice fermion formulation, there are a number of goals to be considered: doubling should be avoided; even at finite lattice spacing a, we want to represent chiral symmetry in a sound way; and we are seeking a good scaling behavior. Conceptually we have to require locality (the lattice Dirac operator D(x, y, U) has to decay at least exponentially in |x — y|). In addition, for practical purposes we desire a high level of locality, i.e. a fast exponential decay or even ultralocality (which means that the couplings in D drop to zero beyond a finite number of lattice spacings). A further issue is a good approximation to rotation invariance. Last but not least, the formulation should be simple enough to allow for efficient simulations. Here we report on a construction, which is designed to do justice to all of these goals.