Spectral properties of the Landau gauge Faddeev-Popov operator in lattice gluodynamics

TL;DR

This paper investigates the spectral properties of the Faddeev-Popov operator in lattice gluodynamics, revealing how eigenvalue distributions relate to the ghost propagator and the Gribov problem.

Contribution

It provides new insights into the eigenvalue spectrum of the Faddeev-Popov operator at different lattice sizes and couplings, highlighting the role of low-lying eigenmodes in the ghost propagator.

Findings

Eigenvalues accumulate near zero with increasing volume.

Approximately 200 eigenmodes suffice to reproduce the ghost propagator at lowest momentum.

Large ghost propagator values are linked to contributions from low-lying eigenmodes.

Abstract

Recently we reported on the infrared behavior of the Landau gauge gluon and ghost dressing functions in SU(3) Wilson lattice gluodynamics with special emphasis on the Gribov problem. Here we add an investigation of the spectral properties of the Faddeev-Popov operator at $\beta$=5.8 and 6.2 for lattice sizes 12^4, 16^4 and 24^4. The larger the volume the more of its eigenvalues are found accumulated close to zero. Using the eigenmodes for the spectral representation it turns out that for our smallest lattice O(200) eigenmodes are sufficient to saturate the ghost propagator at lowest momentum. We associate exceptionally large values of the ghost propagator to extraordinary contributions of low-lying eigenmodes.