Taste-splittings of staggered, Karsten-Wilczek and Borici-Creutz fermions under gradient flow in 2D

TL;DR

This paper investigates the taste-splitting phenomena of staggered, Karsten-Wilczek, and Borici-Creutz fermions in 2D using gradient flow, focusing on eigenvalue spectra and spectroscopic quantities to understand their near-degeneracy.

Contribution

It provides a comparative analysis of taste-splittings in different fermion formulations under gradient flow in 2D, highlighting their spectral similarities and differences.

Findings

Eigenvalue spectra show near-degeneracy among the fermion types.

Gradient flow affects the spectral properties and taste-splitting.

Spectroscopic quantities reflect the degeneracy observed in eigenvalues.

Abstract

Karsten-Wilczek and Borici-Creutz fermions show a near-degeneracy of the $2$ species involved, similar to the $2^{d/2}$ species of staggered fermions. Hence in $d=2$ dimensions all three formulations happen to be minimally doubled (two species). This near-degeneracy shows up both in the eigenvalue spectrum of the respective Dirac operator and in spectroscopic quantities (e.g. the pion mass), but in the former case it is easier to quantify. We use the quenched Schwinger model to determine the low-lying eigenvalues of these fermion operators at a fixed gradient flow time $\tau$ (either in lattice units or in physical units, hence keeping either $\tau/a^2$ or $e^2 \tau$ fixed at all $\beta$).