Stability of lattice QCD simulations and the thermodynamic limit

Debbio, Luigi Del; Giusti, Leonardo; Lüscher, Martin; Petronzio, R.; Tantalo, Nazario

doi:10.1088/1126-6708/2006/02/011

Cited by 148 publications

(271 citation statements)

References 27 publications

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“…In infinite volume the ratio is the renormalization factor Z A , which we expect to be near 1 with nHYP fermions. On large but finite volume the ratio might not have any physical meaning, but there is indication that in practice it remains close to Z A [6]. Our large volume runs givē µ/m P CAC ≈ 0.82, while the ratio here is 1.1, showing the effect of the finite volume.…”

Section: Numerical Testsmentioning

confidence: 65%

Reweighting towards the chiral limit

2008

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We propose to perform fully dynamical simulations at small quark masses by reweighting in the quark mass. This approach avoids some of the technical difficulties associated with direct simulations at very small quark masses. We calculate the weight factors stochastically, using determinant breakup and low mode projection to reduce the statistical fluctuations. We find that the weight factors fluctuate only moderately on nHYP smeared dynamical Wilson-clover ensembles, and we could successfully reweight 16 4 , (1.85fm) 4 volume configurations from m q ≈ 20MeV to m q ≈ 5MeV quark masses, reaching the ǫ−regime. We illustrate the strength of the method by calculating the low energy constant F from the ǫ−regime pseudo-scalar correlator.

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Section: Numerical Testsmentioning

confidence: 65%

Reweighting towards the chiral limit

2008

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“…has a universal continuum limit [31]. The same applies to the spectral density ρ ν (λ) defined in the theory at fixed topology.…”

Section: Jhep04(2007)090mentioning

confidence: 88%

“…We introduce numerical estimators of the condensate which are infrared stable and free from mass-dependent additive ultraviolet divergences. This progress builds on the recent understanding of the renormalization properties of the spectral density of the Dirac operator [31]. The form of these estimators represents and explicit example of how the informations from the chiral effective theory can be used not only for the interpretation/extrapolation of the data, but also to design more efficient numerical algorithms.…”

Section: Jhep04(2007)090mentioning

confidence: 99%

Spontaneous chiral symmetry breaking in QCD: a finite-size scaling study on the lattice

Giusti¹,

Necco²

2007

J. High Energy Phys.

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Spontaneous chiral symmetry breaking in QCD with massless quarks at infinite volume can be seen in a finite box by studying, for instance, the dependence of the chiral condensate from the volume and the quark mass. We perform a feasibility study of this program by computing the quark condensate on the lattice in the quenched approximation of QCD at small quark masses. We carry out simulations in various topological sectors of the theory at several volumes, quark masses and lattice spacings by employing fermions with an exact chiral symmetry, and we focus on observables which are infrared stable and free from mass-dependent ultraviolet divergences. The numerical calculation is carried out with an exact variance-reduction technique, which is designed to be particularly efficient when spontaneous symmetry breaking is at work in generating a few very small low-lying eigenvalues of the Dirac operator. The finite-size scaling behaviour of the condensate in the topological sectors considered agrees, within our statistical accuracy, with the expectations of the chiral effective theory. Close to the chiral limit we observe a detailed agreement with the first Leutwyler-Smilga sum rule. By comparing the mass, the volume and the topology dependence of our results with the predictions of the chiral effective theory, we extract the corresponding low-energy constant.

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“…This is another reason why we update F W in the inner-most loop in Eq. (26), in addition to its consistency with the updated gauge field described in Sec. 3.…”

Section: Properties Of Hmcmentioning

confidence: 93%

Two-flavor QCD simulation with exact chiral symmetry

et al. 2008

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We perform numerical simulations of lattice QCD with two flavors of dynamical overlap quarks, which have exact chiral symmetry on the lattice. While this fermion discretization is computationally demanding, we demonstrate the feasibility to simulate reasonably large and fine lattices by a careful choice of the lattice action and algorithmic improvements. Our production runs are carried out on a 16 3 × 32 lattice at a single lattice spacing around 0.12 fm. We explore the sea quark mass region down to m s /6, where m s is the physical strange quark mass, for a good control of the chiral extrapolation in future calculations of physical observables. We describe in detail our setup and algorithmic properties of the production simulations and present results for the static quark potential to fix the lattice scale and the locality of the overlap operator.

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Stability of lattice QCD simulations and the thermodynamic limit

Cited by 148 publications

References 27 publications

Reweighting towards the chiral limit

Reweighting towards the chiral limit

Spontaneous chiral symmetry breaking in QCD: a finite-size scaling study on the lattice

Two-flavor QCD simulation with exact chiral symmetry

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