Disconnected Loop Subtraction Methods in Lattice QCD

Lattice QCD calculations of disconnected quark loop operators are extremely computer time-consuming to evaluate. To compute these diagrams using lattice techniques, one generally uses stochastic noise methods. These employ a randomly generated set of noise vectors to project out physical signals. In order to strengthen the signal in these calculations, various noise subtraction techniques may be employed. In addition to the standard method of perturbative subtraction, one may also employ matrix deflation techniques using the GMRES-DR and MINRES-DR algorithms as well as polynomial subtraction techniques to reduce statistical uncertainty. Our matrix deflation methods play two roles: they both speed up the solution of the linear equations as well as decrease numerical noise. We show how to combine deflation with either perturbative and polynomial methods to produce extremely powerful noise suppression algorithms. We use a variety of lattices to study the effects. In order to set a benchmark, we first use the Wilson matrix in the quenched approximation. We see strong low eigenmode dominance at kappa critical ($\kappa_{crit}$) in the variance of the vector and scalar operators. We also use MILC dynamic lattices, where we observe deflation subtraction results consistent with the effectiveness seen in the quenched data.