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

Abstract

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 $p\simeq 2$ with smearing and $p=1$ without), while Karsten-Wilczek and Boriçi-Creutz fermions scale as ${\delta }_{\mathrm{ntm}}\propto a$ (regardless of the smearing level). Large logarithmic corrections are seen with smearing.

Comments: 23 pages, 19 figures