Smearing and filtering methods in lattice QCD - a quantitative comparison

TL;DR

This paper systematically compares three filtering methods in lattice QCD to extract topological excitations, demonstrating their tunability and revealing similar structures with a power-law relation.

Contribution

It provides a quantitative comparison of smearing, Laplace filtering, and fermionic filtering, showing their equivalence over a range of parameters in lattice QCD.

Findings

All methods can be tuned to each other across filtering levels.

They reveal similar topological structures in lattice configurations.

A power-law relates the number and packing fraction of topological clusters.

Abstract

We systematically compare three filtering methods used to extract topological excitations from lattice gauge configurations, namely smearing, Laplace filtering and the filtered fermionic topological charge (with chirally improved fermions). Each of these techniques introduces ambiguities, like its parameter dependence. We show, however, that all these methods can be tuned to each other over a broad range of filtering levels and that they reveal very similar topological structures. For these common structures we find an interesting power-law relating the number and packing fraction of clusters of filtered topological charge.