Domain decomposition, multi-level integration and exponential noise reduction in lattice QCD

TL;DR

This paper presents a novel approach combining domain decomposition and multi-level integration to compute fermionic correlators in lattice QCD, significantly improving the signal-to-noise ratio for challenging observables.

Contribution

It introduces a hierarchical expansion of the quark propagator enabling multi-level Monte Carlo integration in lattice QCD calculations.

Findings

Exponential increase in signal-to-noise ratio observed

Effective factorization of gauge-field dependence

Successful application to disconnected correlators and nucleon two-point functions

Abstract

We explore the possibility of computing fermionic correlators on the lattice by combining a domain decomposition with a multi-level 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 multi-level 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 cases we observe a significant exponential increase of the signal-to-noise ratio.