Fermion simulations using parallel transported multigrid

Using a parallel transported multigrid (PTMG) technique, we compute the chiral symmetry order parameter and the pseudo-scalar meson mass in the quenched Schwinger model. In our PTMG method, the coarse level gauge and "fermionic" fields are derived from the fine level fields using the appropriate gauge fields as parallel transporters. For small quark masses and moderate correlation lengths we obtain a very rapid convergence (about one order of magnitude per cycle). In the same range of parameters, the one-level relaxation algorithms are slower by many orders of magnitude. We then show how to use this solver for dynamical fermions.