Fermions as Global Correction: the QCD Case

TL;DR

This paper introduces a hierarchical algorithm for treating fermion determinants in lattice QCD, enabling efficient global acceptance-rejection steps by separating ultraviolet and infrared modes and reducing stochastic noise.

Contribution

It presents a novel recursive domain decomposition approach that improves the feasibility of global fermion determinant updates in lattice QCD simulations.

Findings

High global acceptance rates on moderate lattice sizes

Effective hierarchical filtering reduces stochastic noise

Demonstrates practical viability of the method

Abstract

It is widely believed that the fermion determinant cannot be treated in global acceptance-rejection steps of gauge link configurations that differ in a large fraction of the links. However, for exact factorizations of the determinant that separate the ultraviolet from the infrared modes of the Dirac operator it is known that the latter show less variation under changes of the gauge field compared to the former. Using a factorization based on recursive domain decomposition allows for a hierarchical algorithm that starts with pure gauge updates of the links within the domains and ends after a number of filters with a global acceptance-rejection step. Ratios of determinants have to be treated stochastically and we construct techniques to reduce the noise. We find that the global acceptance rate is high on moderate lattice sizes and demonstrate the effectiveness of the hierarchical filter.