Multi-level integration for meson propagators

Abstract

The computation of many correlation functions in lattice QCD is severely hindered by a signal-tonoise problem. Recent developments in the factorization of both the fermion propagator and determinant pave the way for the implementation of multi-level Monte Carlo integration techniques for lattice QCD. In these proceedings we introduce new strategies for the estimation of the factorized contribution to the connected and disconnected diagrams for meson two-point functions. An estimator for the factorized connected diagram is constructed sequentially for a two-level integration scheme. For the disconnected diagram, we introduce an improved estimator by performing a frequency-splitting of traces, applicable with or without multi-level integration. Preliminary results in the quenched theory with a two-level integration scheme are presented.

Frequency-splitting estimators of single-propagator traces

“…A more efficient scheme, already outlined in Ref. [31], is depicted in the right-hand panel of Fig. 8, where even-odd blocks of half the linear size of the previous ones are introduced.…”