Parallel-transported multigrid and its application to the schwinger model

We present an efficient multigrid algorithm to invert the Dirac-Operator in simulations of lattice gauge theories. The coarse-level gauge and "fermionic" fields are derived from the fine-level fields using the appropriate gauge fields as parallel transporters; for this reason the method is called Parallel-Transported Multigrid (PTMG). We demonstrate the algorithm by computing the chiral symmetry order parameter and the pseudoscalar meson mass in the quenched Schwinger Model. In a considerable part of the physically relevant parameter space the method is superior over the one-level relaxation algorithms by several orders of magnitude. The method can be generalized in a straightforward way to SU(3) lattice gauge theory in 4 dimensions.