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Locality of the fourth root of the Staggered-fermion determinant: renormalization-group approach

Yigal Shamir
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Abstract

Consistency of present-day lattice QCD simulations with dynamical (``sea'') staggered fermions requires that the determinant of the staggered-fermion Dirac operator, $det(D)$, be equal to $det^4(D_{rg}) det(T)$ where $D_{rg}$ is a local one-flavor lattice Dirac operator, and $T$ is a local operator containing only excitations with masses of the order of the cutoff. Using renormalization-group (RG) block transformations I show that, in the limit of infinitely many RG steps, the required decomposition exists for the free staggered operator in the ``flavor representation.'' The resulting one-flavor Dirac operator $D_{rg}$ satisfies the Ginsparg-Wilson relation in the massless case. I discuss the generalization of this result to the interacting theory.

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Yigal Shamir. 2004-12-08. Locality of the fourth root of the Staggered-fermion determinant: renormalization-group approach. https://doi.org/10.1103/physrevd.71.034509

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