Discretisation Errors in Landau Gauge on the Lattice

Bonnet, Frédéric; Bowman, Patrick O.; Leinweber, Derek B.; Williams, Anthony G.; Richards, David

doi:10.1071/ph99047

Cited by 40 publications

(46 citation statements)

References 6 publications

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“…We fix to Landau gauge by maximizing the Oða 2 Þ improved gauge fixing functional [35] (34) using a Fourier transform accelerated algorithm [35][36][37][38]. To avoid Gribov copy issues, we first gauge fix configurations with 100 sweeps of smearing and then use these as a preconditioner for the same configurations with lower levels of smearing [39].…”

Section: Resultsmentioning

confidence: 99%

Quark propagation in the instantons of lattice QCD

et al. 2013

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We quantitatively examine the extent to which instanton degress of freedom, contained within standard Monte-carlo generated gauge-field configurations, can maintain the characteristic features of the mass and renormalisation functions of the non-perturbative quark propagator. We use overimproved stout-link smearing to isolate instanton effects on the lattice. Using a variety of measures, we illustrate how gauge fields consisting almost solely of instanton-like objects are produced after only 50 sweeps of smearing. We find a full vacuum, with a packing fraction more than three times larger than phenomenological models predict. We calculate the overlap quark propagator on these smeared configurations, and find that even at high levels of smearing the majority of the characteristic features of the propagator are reproduced. We thus conclude that instantons contained within standard Monte-carlo generated gauge-field configurations are the degrees of freedom responsible for the dynamical generation of mass observed in lattice QCD.

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Section: Resultsmentioning

confidence: 99%

Quark propagation in the instantons of lattice QCD

et al. 2013

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“…Landau gauge fixing is performed by enforcing the Lorentz gauge condition, P @ A x 0 on a configuration by configuration basis. For the tadpole improved plaquette plus rectangle (Lüscher-Weisz [21]) gauge action which we use in the current work, we use the O a 2 improved gauge-fixing scheme, this is achieved by maximizing the functional [22],…”

Section: Gauge-fixingmentioning

confidence: 99%

“…Landau gauge fixing to the gauge configuration was done using a Conjugate Gradient Fourier Acceleration [31] algorithm with an accuracy of P j@ A x j 2 < 10 ÿ12 . The improved gauge-fixing scheme was used to minimize gauge-fixing discretization errors [22]. For the Laplacian gauge fixing, we only use the @ 2 (II) gauge [19].…”

Section: A Simulation Parametersmentioning

confidence: 99%

Quark propagator in Landau and Laplacian gauges with overlap fermions

et al. 2005

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The properties of the momentum space quark propagator in Landau gauge and Gribov copy free Laplacian gauge are studied for the overlap quark action in quenched lattice QCD. Numerical calculations are done on two lattices with different lattice spacing $a$ and the same physical volume. We have calculated the nonperturbative wave function renormalization function $Z(q)$ and the nonperturbative mass function $M(p)$ for a variety of bare quark masses and perform a simple linear extrapolation to the chiral limit. We focus on the comparison of the behavior of $Z(q)$ and $M(p)$ in the chiral limit in the two gauge fixing schemes as well as the behavior on two lattices with different lattice spacing $a$. We find that the mass functions $M(p)$ are very similar for the two gauges while the wave-function renormalization function $Z(q)$ is more strongly infrared suppressed in the Laplacian gauge than in the Landau gauge on the finer lattice. For Laplacian gauge, it seems that the finite $a$ error is large on the coarse lattice which has a lattice spacing $a$ of about 0.124 fm.Comment: 8 pages, 6 figures, version appeared in Phys. Rev.

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“…as described in [10]. We employ a Conjugate Gradient, Fourier Accelerated gauge fixing algorithm [11] optimally designed for parallel machines.…”

Section: O(a 2 ) Improvementmentioning

confidence: 99%

Infrared behavior of the gluon propagator on a large volume lattice

et al. 2000

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The first calculation of the gluon propagator using an O(a 2 ) improved action with the corresponding O(a 2 ) improved Landau gauge fixing condition is presented. The gluon propagator obtained from the improved action and improved Landau gauge condition is compared with earlier unimproved results on similar physical lattice volumes of 3.2 3 × 6.4 fm 4 . We find agreement between the improved propagator calculated on a coarse lattice with lattice spacing a = 0.35 fm and the unimproved propagator calculated on a fine lattice with spacing a = 0.10 fm. This motivates us to calculate the gluon propagator on a coarse large-volume lattice 5.6 3 × 11.2 fm 4 . The infrared behavior of previous studies is confirmed in this work. The gluon propagator is enhanced at intermediate momenta and suppressed at infrared momenta. Therefore the observed infrared suppression of the Landau gauge gluon propagator is not a finite volume effect.

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Discretisation Errors in Landau Gauge on the Lattice

Cited by 40 publications

References 6 publications

Quark propagation in the instantons of lattice QCD

Quark propagation in the instantons of lattice QCD

Quark propagator in Landau and Laplacian gauges with overlap fermions

Infrared behavior of the gluon propagator on a large volume lattice

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