Eigenvalue based taste breaking of staggered, Karsten-Wilczek and Borici-Creutz fermions with stout smearing in the Schwinger model

In two spacetime dimensions staggered fermions are minimally doubled, like Karsten-Wilczek and Borici-Creutz fermions. A continuum eigenvalue is thus represented by a pair of near-degenerate eigenvalues, with the splitting $\delta$ quantifying the cut-off induced taste symmetry breaking. We use the quenched Schwinger model to determine the low-lying fermionic eigenvalues (with 0, 1 or 3 steps of stout smearing), and analyze them in view of the global topological charge $q\in\mathbb{Z}$ of the gauge background. For taste splittings pertinent to would-be zero modes, we find asymptotic Symanzik scaling of the form $\delta_\mathrm{wzm} \propto a^2$ with link smearing, and $\delta_\mathrm{wzm} \propto a$ without, for each action. For taste splittings pertinent to non-topological modes, staggered splittings scale as $\delta_\mathrm{ntm} \propto a^p$ (where $p\simeq2$ with smearing and $p=1$ without), while Karsten-Wilczek and Bori\c{c}i-Creutz fermions scale as $\delta_\mathrm{ntm} \propto a$ (regardless of the smearing level). Large logarithmic corrections are seen with smearing.