Minimally doubled fermions and topology in 2D

TL;DR

This paper investigates how different lattice fermion formulations in 2D perceive topological charge, showing that minimally doubled fermions can be made topology-aware through specific modifications.

Contribution

It demonstrates that minimally doubled fermions are initially insensitive to topology but can be adapted to detect topological charge via a species-splitting term.

Findings

Minimally doubled fermions are insensitive to topology without modification.

A species-splitting term can make these fermions topology-aware.

Eigenvalue spectra and chiralities are used to analyze topological perception.

Abstract

We use the two-dimensional Schwinger model to investigate how lattice fermions perceive the global topological charge $q\in\mathbf{Z}$ of a given gauge background $U$. After a warm-up part devoted to staggered, Adams, Wilson and naive fermions, we consider Karsten-Wilczek and Borici-Creutz fermions, which are in the class of minimally doubled lattice fermion actions. We focus on the eigenvalue spectrum and the chiralities of the pertinent eigenmodes. Without modification both minimally doubled actions are found to be insensitive to topology, but in either case it is possible to define a suitable species-splitting term to make the resulting operator topology aware.