The scaling dimension of low lying Dirac eigenmodes and of the topological charge density

TL;DR

This paper investigates how the localization of low-lying Dirac eigenmodes and topological charge density relates to different topological objects in lattice gauge theories by analyzing their scaling behavior across various lattice spacings and volumes.

Contribution

It introduces a scaling analysis method to quantify the presence and correlation of various topological objects with eigenmode localization in lattice QCD.

Findings

Different topological objects have distinct co-dimensions affecting localization.

Scaling analysis reveals the relative abundance of topological objects.

Correlation between eigenmodes and topological structures is characterized.

Abstract

As a quantitative measure of localization, the inverse participation ratio of low lying Dirac eigenmodes and topological charge density is calculated on quenched lattices over a wide range of lattice spacings and volumes. Since different topological objects (instantons, vortices, monopoles, and artifacts) have different co-dimension, scaling analysis provides information on the amount of each present and their correlation with the localization of low lying eigenmodes.