Properties of near-zero modes and chiral symmetry breaking
Christof Gattringer, Meinulf Goeckeler, P.E.L. Rakow, Stefan Schaefer, and Andreas Schaefer
TL;DR
This paper investigates the localization and chirality of eigenvectors of the lattice Dirac operator, exploring how near-zero modes transition into bulk modes, and supports the instanton-based explanation of chiral symmetry breaking.
Contribution
It provides a detailed analysis of eigenvector properties and their dependence on eigenvalues, using a systematic Dirac operator expansion to support the instanton model of chiral symmetry breaking.
Findings
Near-zero modes transition into bulk modes with increasing eigenvalues
Results support instanton-anti-instanton interactions as key for chiral symmetry breaking
Eigenvector properties vary with eigenvalue size, indicating a transition in mode localization
Abstract
We study localization and chirality properties of eigenvectors of the lattice Dirac operator. In particular we focus on the dependence of our observables on the size of the corresponding eigenvalue, which allows us to study the transition of a near-zero mode into a bulk mode. We analyze ensembles of quenched SU(3) configurations using a Dirac operator which is a systematic expansion in path length of a solution of the Ginsparg-Wilson equation. Our results support the interpretation of the excitations relevant for chiral symmetry breaking as interacting instantons and anti-instantons.
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