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Dürr, Stephan; Hoelbling, Christian

doi:10.1103/physrevd.69.034503

Cited by 71 publications

(91 citation statements)

References 42 publications

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“…the vanishing of the condensate in one-flavor QCD). This point has been discussed in our earlier paper [18] and elsewhere [2,3,19,23,30,32]. We assume throughout this paper that the order of limits has been taken correctly, so that the RCT has positive quark mass, which may only be taken to zero as a final step.…”

Section: Introductionmentioning

confidence: 91%

“…In the continuum, the determinant of D + m is then (formally) positive; the determinant is rigorously positive for overlap quarks. 3 We thus have…”

Section: Rooted Correlation Functions In the Continuum Limitmentioning

confidence: 99%

“…[2,18]. If on the contrary, the chiral limit is taken first, while keeping a = 0, the finite-volume condensate will vanish [2,3]. The emergence of a non-zero chiral condensate in the Schwinger model with rooted staggered fermions, including the non-commutativity of the continuum and chiral limit, was carefully checked numerically in Ref.…”

Section: Ward Identitiesmentioning

confidence: 99%

“…[3] to [29]), and there is mounting evidence, both analytical and numerical, that the continuum limit of rooted staggered QCD is in the correct universality class.…”

Section: Introductionmentioning

confidence: 99%

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’t Hooft vertices, partial quenching, and rooted staggered QCD

et al. 2008

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We discuss the properties of 't Hooft vertices in partially quenched and rooted versions of QCD in the continuum. These theories have a physical subspace, equivalent to ordinary QCD, that is contained within a larger space that includes many unphysical correlation functions. We find that the 't Hooft vertices in the physical subspace have the expected form, despite the presence of unphysical 't Hooft vertices appearing in correlation functions that have an excess of valence quarks (or ghost quarks). We also show that, due to the singular behavior of unphysical correlation functions as the massless limit is approached, order parameters for non-anomalous symmetries can be non-vanishing in finite volume if these symmetries act outside of the physical subspace. Using these results, we demonstrate that arguments recently given by Creutz-claiming to disprove the validity of rooted staggered QCD-are incorrect. In particular, the unphysical 't Hooft vertices do not present an obstacle to the recovery of taste symmetry in the continuum limit.

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Section: Introductionmentioning

confidence: 91%

“…In the continuum, the determinant of D + m is then (formally) positive; the determinant is rigorously positive for overlap quarks. 3 We thus have…”

Section: Rooted Correlation Functions In the Continuum Limitmentioning

confidence: 99%

Section: Ward Identitiesmentioning

confidence: 99%

“…[3] to [29]), and there is mounting evidence, both analytical and numerical, that the continuum limit of rooted staggered QCD is in the correct universality class.…”

Section: Introductionmentioning

confidence: 99%

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’t Hooft vertices, partial quenching, and rooted staggered QCD

et al. 2008

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“…We compare (rooted) staggered to overlap fermions [4], both actions defined with one step of APE smearing. For details see [5,6]. Throughout, we use the coupling e to define the physical scale and set the lattice spacing to a = 1.…”

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confidence: 99%

Lattice fermions with complex mass

Dürr

Hoelbling

2006

Phys. Rev. D

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We present evidence in the Schwinger model that rooted staggered fermions may correctly describe the m < 0 sector of a theory with an odd number of flavors. We point out that in QCD-type theories with a complex-valued quark mass every non-chiral action essentially "borrows" knowledge about the θ-transformation properties from the overlap action.The staggered fermion operator D st describes N t = 2 d/2 flavors ("tastes") of quarks in d dimensions. In order to obtain a single quark flavor in dynamical fermion simulations, it has become customary to include the N t -th root of the staggered determinant as a weight factor.In a recent preprint [1] Creutz has argued that this procedure makes it difficult to obtain the right continuum limit. His argument is based on the observation that the staggered determinant is strictly a function of m 2 , whereas the determinant of a true single flavor theory also contains odd powers of m, arising from the unpaired chiral modes of the Dirac operator.In a reply [2] Bernard et al. have noted that the rooted determinant always corresponds to a theory with positive fermion mass, regardless of the sign of the staggered mass term. In addition, they point out that rooting is a non-analytic procedure. Accordingly, they discuss how taking the continuum limit first can lead to odd powers of |m|.In this note we want to address how two observables, the chiral condensate and the topological susceptibility, behave for non-positive quark masses. We demonstrate in the Schwinger model [3] that even with rooted staggered fermions these quantities can be measured for m < 0, by simply reinserting the phase information which gets lost by starting with a doubled action and taking the square-root. This "recipe" can be justified by reference to the overlap action, but it is beyond the realm of a purely Lagrangian approach with staggered fermions.The numerical data presented below are based on a sample of 1000 gauge configurations at β = 9.8 on a N ×N = 28 2 lattice. We compare (rooted) staggered to overlap fermions [4], both actions defined with one step of APE smearing. For details see [5,6]. Throughout, we use the coupling e to define the physical scale and set the lattice spacing to a = 1.First, we consider the scalar condensate. We are interested in its continuum limit in a fixed physical volume (cf. [6]), and for N f = 1 its presence is due to the anomaly [3] and does thus not signal spontaneous symmetry breaking. For overlap fermions and m > 0 its bare version is(1) where the sum runs over all eigenvalues of the massless operator D ov , except for the doublers (on topologically non-trivial backgrounds) at 2ρ. Here, ρ is a parameter in the overlap construction which in our runs is set to 1. The measure in (1) 1

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Numerical properties of staggered quarks with a taste-dependent mass term

Forcrand

Kurkela

Panero

2012

J. High Energ. Phys.

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The numerical properties of staggered Dirac operators with a taste-dependent mass term proposed by Adams [1,2] and by Hoelbling [3] are compared with those of ordinary staggered and Wilson Dirac operators. In the free limit and on (quenched) interacting configurations, we consider their topological properties, their spectrum, and the resulting pion mass. Although we also consider the spectral structure, topological properties, locality, and computational cost of an overlap operator with a staggered kernel, we call attention to the possibility of using the Adams and Hoelbling operators without the overlap construction. In particular, the Hoelbling operator could be used to simulate two degenerate flavors without additive mass renormalization, and thus without fine-tuning in the chiral limit.

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Staggered versus overlap fermions: A study in the Schwinger model withNf=0,1,2

Cited by 71 publications

References 42 publications

’t Hooft vertices, partial quenching, and rooted staggered QCD

’t Hooft vertices, partial quenching, and rooted staggered QCD

Lattice fermions with complex mass

Numerical properties of staggered quarks with a taste-dependent mass term

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