Domain decomposition, multilevel integration, and exponential noise reduction in lattice QCD

We explore the possibility of computing fermionic correlators on the lattice by combining a domain decomposition with a multilevel integration scheme. The quark propagator is expanded in series of terms with a well-defined hierarchical structure. The higher the order of a term, the (exponentially) smaller its magnitude, the less local is its dependence on the gauge field. Once inserted in a Wick contraction, the gauge-field dependence of the terms in the resulting series can be factorized so that it is suitable for multilevel Monte Carlo integration. We test the strategy in quenched QCD by computing the disconnected correlator of two flavor-diagonal pseudoscalar densities, and a nucleon two-point function. In either case we observe a significant exponential increase of the signal-to-noise ratio.