Low-lying Dirac eigenmodes and monopoles in 3+1D compact QED

TL;DR

This paper investigates the behavior of low-lying Dirac eigenmodes in quenched compact QED across different temperatures, revealing their spatial localization, correlation with monopoles, and spectral transition characteristics.

Contribution

It provides new insights into the spatial and spectral properties of Dirac modes in compact QED, especially their relation to monopoles and phase transition effects.

Findings

Near-zero modes anti-correlate with monopole currents

Modes lose temporal structure above T_c and become more localized

Eigenvalue spacing shows a Wigner-Poisson transition

Abstract

We study the properties of low-lying Dirac modes in quenched compact QED at $\beta =1.01$, employing $12^3\times N_t$ ($N_t =4,6,8,10,12$) lattices and the overlap formalism for the fermion action. We pay attention to the spatial distributions of low-lying Dirac modes below and above the ``phase transition temperature'' $T_c$. Near-zero modes are found to have universal anti-correlations with monopole currents, and are found to lose their temporal structures above $T_c$ exhibiting stronger spatial localization properties. We also study the nearest-neighbor level spacing distribution of Dirac eigenvalues and find a Wigner-Poisson transition.