Abelian and non-Abelian Berry curvatures in lattice QCD

TL;DR

This paper investigates the Berry curvature in lattice QCD, analyzing both Abelian and non-Abelian cases for Dirac fermions, with analytical and numerical methods, highlighting effects of interactions and degeneracy loss.

Contribution

It provides the first detailed calculation of Abelian Berry curvature in lattice QCD and compares it with non-Abelian cases for free Dirac fermions.

Findings

Non-Abelian Berry curvature is analytically and numerically computed for free Dirac fermions.

Interacting Dirac fermions in QCD exhibit Abelian Berry curvature due to degeneracy loss.

The study highlights the impact of gluon interactions on Berry curvature properties.

Abstract

We studied the Berry curvature of the massive Dirac fermion in 3+1 dimensions. For the non-interacting Dirac fermion, the Berry curvature is non-Abelian because of the degeneracy of positive and negative helicity modes. We calculated the non-Abelian Berry curvature analytically and numerically. For the interacting Dirac fermion in QCD, the degeneracy is lost because gluons carry helicity and color charge. We calculated the Abelian Berry curvature in lattice QCD.