Inverting the Dirac matrix for SU(2) lattice gauge theory by means of parallel transported multigrid

We compare the convergence rates for inverting the Dirac matrix of a non-abelian gauge theory by the parallel transported multigrid algorithm (PTMG) and by the conjugate gradient (CG) approach. The test is carried out for SU(2) lattice gauge theory in two dimensions. The gauge field configurations are generated in the quenched approximation for various values of the gauge field correlation length ξ(β). We have performed runs for three different lattice sizes with the ratio ξ/L kept fixed; L denotes the linear dimension of the square lattices used. As L increases, the PTMG becomes more and more efficient. On a 256×256 lattice with the bare quark mass mbare = 0.0005 and ξ = 20, the PTMG is at least ten times faster than the CG. It seems reasonable to expect similar results also in four dimensions.