PROJECTIVE MULTIGRID FOR WILSON FERMIONS

We propose a multi-level algorithm for Wilson fermions in a background gauge field by the application of the projective multigrid method. A variational wave function is placed on blocks of 2d sites which gives an effective Dirac equation for coarser lattices with new effective gauge links. Renormalization group arguments are given to motivate our Ansatz. Finally we test the multi-level algorithm on a 2d U(1) lattice gauge theory and show that critical slowing down is eliminated for distances less than the confinement scale l-sigma defined by the string tension. As the quark mass vanishes convergence is accelerated by a factor of this length l-sigma measured in lattice units.