Localization properties of the topological charge density and the low lying eigenmodes of overlap fermions

TL;DR

This paper investigates the topological charge density and low-lying eigenmodes of overlap fermions in lattice QCD, revealing the structure and dimensionality of topological features using UV filtering and correlation functions.

Contribution

It provides new insights into the topological structures of the QCD vacuum by analyzing eigenmodes and charge densities with UV filtering, highlighting their complex, tangled nature.

Findings

Density exhibits sign-coherent structures that become more tangled with more modes

Two-point correlation function shows increasing negative tail indicating complex structure

Eigenmodes' inverse participation ratio suggests specific dimensionality of topological features

Abstract

Overlap fermions, which preserve exact chiral symmetry on the lattice, provide a powerful tool for investigating the topological structure of the vacuum. Applying this formulation to zero-temperature quenched SU(3) configurations generated by means of the Luescher-Weisz action, we define the topological charge density with and without UV filtering and study its properties by looking at the density profile and the two-point correlation function. We observe that the density possesses global sign coherent structures, which get increasingly tangled as more and more modes are included. This change of the structure is also detected by the increasing negative tail of the two-point function. We also study the inverse participation ratio of the eigenmodes and discuss their dimensionality.