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

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.