Local coherence and deflation of the low quark modes in lattice QCD

TL;DR

This paper investigates the local coherence of low quark modes in lattice QCD and develops a deflation technique that significantly speeds up quark propagator calculations by exploiting this coherence.

Contribution

It introduces a local deflation method for low quark modes in lattice QCD, enabling efficient computation with linear volume scaling.

Findings

Achieves large speed-up factors in quark propagator calculations.

Demonstrates flat scaling behavior with respect to quark mass.

Validates the local coherence of low quark modes in numerical studies.

Abstract

The spontaneous breaking of chiral symmetry in QCD is known to be linked to a non-zero density of eigenvalues of the massless Dirac operator near the origin. Numerical studies of two-flavour QCD now suggest that the low quark modes are locally coherent to a certain extent. As a consequence, the modes can be simultaneously deflated, using local projectors, with a total computational effort proportional to the lattice volume (rather than its square). Deflation has potentially many uses in lattice QCD. The technique is here worked out for the case of quark propagator calculations, where large speed-up factors and a flat scaling behaviour with respect to the quark mass are achieved.