Fermions as global correction in lattice QCD

TL;DR

This paper proposes a hierarchical algorithm for lattice QCD that uses a factorization of the fermion determinant to improve acceptance rates and potentially address critical slowing down.

Contribution

It introduces a recursive domain decomposition-based factorization method enabling a hierarchical approach to include fermions in lattice QCD simulations.

Findings

High global acceptance rates on moderate lattice sizes.

Potential to mitigate critical slowing down in lattice QCD.

Hierarchical algorithm combining local updates with global acceptance.

Abstract

The fermion determinant is a highly non-local object and its logarithm is an extensive quantity. For these reasons it is widely believed that the determinant cannot be treated in acceptance steps of gauge link configurations that differ in a large fraction of the links. However, for exact factorisations of the determinant that separate the ultraviolet from the infra-red 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 factorisation 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 step. We find that the global acceptance rate is high on moderate lattice sizes. Whether this type of algorithm can help in curing the problem of critical slowing down is presently under study.