Locality and multi-level sampling with fermions

Abstract

Multi-level Monte Carlo sampling techniques exploit the locality of quantum field theory to provide a solution in purely-bosonic quantum field theories to the signal-to-noise ratio problem that affects the lattice determination of a large class of quantities. However, it is not straightforward to generalize multi-level sampling to lattice theories with fermionic content, such as QCD, due to the loss of manifest locality after the fermion path integral is performed. We discuss how the decrease of the fermion propagator with Euclidean distance induces a systematic approximation of the fermion propagator and the fermion determinant, in which the gauge field dependence of distant spacetime regions is completely factorized. This allows us to apply multi-level sampling to the lattice QCD computation of hadronic observables, such as mesonic and baryonic correlators. In particular, we show an application of this strategy to the disconnected contribution to the correlator of two flavour-singlet pseudoscalar densities, which results in a significant increase of the signal-to-noise ratio when a two-level sampling scheme is used.