In the quenched Schwinger model, gradient flow makes staggered fermion taste splittings decay exponentially, but for Karsten-Wilczek and Borici-Creutz fermions only the topological zero-mode splitting decays while other splittings plateau near a|δ|∼10^-3.
The Index Theorem and Universality Properties of the Low-lying Eigenvalues of Improved Staggered Quarks
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abstract
We study various improved staggered quark Dirac operators on quenched gluon backgrounds in lattice QCD generated using a Symanzik-improved gluon action. We find a clear separation of the spectrum into would-be zero modes and others. The number of would-be zero modes depends on the topological charge as expected from the Index Theorem, and their chirality expectation value is large (approximately 0.7). The remaining modes have low chirality and show clear signs of clustering into quartets and approaching the random matrix theory predictions for all topological charge sectors. We conclude that improvement of the fermionic and gauge actions moves the staggered quarks closer to the continuum limit where they respond correctly to QCD topology.
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Taste-splittings of staggered, Karsten-Wilczek and Borici-Creutz fermions under gradient flow in 2D
In the quenched Schwinger model, gradient flow makes staggered fermion taste splittings decay exponentially, but for Karsten-Wilczek and Borici-Creutz fermions only the topological zero-mode splitting decays while other splittings plateau near a|δ|∼10^-3.