Topological properties of minimally doubled fermions in two space-time dimensions

TL;DR

This paper investigates how different lattice fermion operators in two dimensions detect topological charge, revealing that minimally doubled fermions perceive topological charge similarly to staggered and naive fermions.

Contribution

It compares the topological charge perception of minimally doubled fermions with other fermions in the 2D Schwinger model, providing new insights into their spectral properties.

Findings

Karsten-Wilczek and Borici-Creutz fermions perceive topological charge like staggered and naive fermions.

Eigenvalue spectra and chiralities are analyzed for various fermion operators.

Spectral flow analysis supports the similar topological perception among certain fermions.

Abstract

The two-dimensional Schwinger model is used to explore how lattice fermion operators perceive the global topological charge $q \in \mathbb{Z}$ of a given background gauge field. We focus on Karsten-Wilczek and Borici-Creutz fermions, which are minimally doubled, and compare them to Wilson, Brillouin, naive, staggered and Adams fermions. For each operator the eigenvalue spectrum in a background with $q \neq 0$ is determined along with the chiralities of the eigenmodes, and the spectral flow of the pertinent hermitean operator is worked out. We find that Karsten-Wilczek and Borici-Creutz fermions perceive the global topological charge $q$ in the same way as staggered and naive fermions do.