Domain decomposition and multilevel integration for fermions

Understand

The numerical computation of many hadronic correlation functions is exceedingly difficult due to the exponentially decreasing signal-to-noise ratio with the distance between source and sink.

• Multilevel integration methods, using independent updates of separate regions in space-time, are known to be able to solve such problems but have so far been available only for pure gauge theory.
• We present first steps into the direction of making such integration schemes amenable to theories with fermions, by factorizing a given observable via an approximated domain decomposition of the quark propagator.
• This allows for multilevel integration of the (large) factorized contribution to the observable, while its (small) correction can be computed in the standard way.