Low-dimensional long-range topological charge structure in the QCD vacuum

Horváth, I.; Dong, Shao-Jing; Draper, Terrence; Lee, Frank; Liu, K. F.; Mathur, Nilmani; Thacker, H.B.; Zhang, Jianbo

doi:10.1103/physrevd.68.114505

Cited by 100 publications

(201 citation statements)

References 30 publications

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“…From Eqs. (10,12,13,19) it follows that ρ 0 (κ, E, p) is decreasing in E and non-increasing in κ. Moreover, since δ(r, p) is non-decreasing in p, so is ∆ 0 (R, ρ, p), and consequently ρ 0 (κ, E, p).…”

Section: B Parametric Freedom In Statistical Cutoff Removalmentioning

confidence: 99%

“…5 the use of boundary approximants for efficiently computing the "configurations" of overlap-based topological density. This lattice topological field was crucial for identifying the low-dimensional long-range topological structure in QCD vacuum [12]. The insensitivity properties tested here make large scale computations of this type practical since, at fixed accuracy, the cost per configuration is simply proportional to the volume, similarly to the case of generic ultralocal gauge operators.…”

Section: Introductionmentioning

confidence: 99%

“…stable under deformations of the gauge field, directly on the lattice. Indeed, this property was instrumental in finding that, when fluctuations at all scales are included, topological charge in QCD organizes into low-dimensional global structure of space-filling type [12]. The structure takes the form of a double sheet formed by topological densities of opposite sign, and is inherently global [16].…”

Section: Application: Topological Structure In Qcd Vacuummentioning

confidence: 99%

“…Thus, the cost of a×b is one in the former, but diverges at least as log 1/δ, due to increasing bit size of representing real a, b so that precision δ in a×b is achieved. 12 Thus, S and C P also weakly depend on L which can be thought of as already taken to infinity in (36). 13 Note that it is implicitly understood here, as is in (38), that L is sufficiently large (L R ) so that finite-L correction to C P is negligible for in question.…”

Section: Computational Efficiencymentioning

confidence: 99%

“…12 Thus, when replacing the operator with its boundary approximant, the cost of evaluating it via P changes as…”

Section: Computational Efficiencymentioning

confidence: 99%

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Locality and efficient evaluation of lattice composite fields: Overlap-based gauge operators

Alexandru

Horváth

2017

Phys. Rev. D

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We propose a novel general approach to locality of lattice composite fields, which in case of QCD involves locality in both quark and gauge degrees of freedom. The method is applied to gauge operators based on the overlap Dirac matrix elements, showing for the first time their local nature on realistic path-integral backgrounds. The framework entails a method for efficient evaluation of such non-ultralocal operators, whose computational cost is volume-indepenent at fixed accuracy, and only grows logarithmically as this accuracy approaches zero. This makes computation of useful operators, such as overlap-based topological density, practical. The key notion underlying these features is that of exponential insensitivity to distant fields, made rigorous by introducing the procedure of statistical regularization. The scales associated with insensitivity property are useful characteristics of non-local continuum operators.

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Section: B Parametric Freedom In Statistical Cutoff Removalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Application: Topological Structure In Qcd Vacuummentioning

confidence: 99%

Section: Computational Efficiencymentioning

confidence: 99%

“…12 Thus, when replacing the operator with its boundary approximant, the cost of evaluating it via P changes as…”

Section: Computational Efficiencymentioning

confidence: 99%

See 3 more Smart Citations

Locality and efficient evaluation of lattice composite fields: Overlap-based gauge operators

Alexandru

Horváth

2017

Phys. Rev. D

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Topological Structure of the QCD Vacuum Revealed by Overlap Fermions

Ilgenfritz

Koller

Koma

et al. 2010

High Performance Computing in Science and Engineering, Garching/Munich 2009

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Overlap fermions preserve a remnant of chiral symmetry on the lattice. They are a powerful tool to investigate the topological structure of the vacuum of Yang-Mills theory and full QCD. Recent results concerning the localization of topological charge and the localization and local chirality of the overlap eigenmodes are reported. The charge distribution is radically different, if a spectral cut-off for the Dirac eigenmodes is applied. The density q(x) is changing from the scale-a charge density (with full lattice resolution) to the ultraviolet filtered charge density. The scale-a density, computed on the Linux cluster of LRZ, has a singular, sign-coherent global structure of co-dimension 1 first described by the Kentucky group. We stress, however, the cluster properties of the UV filtered topological density resembling the instanton picture. The spectral cut-off can be mapped to a bosonic smearing procedure. The UV filtered field strength reveals a high degree of (anti)selfduality at "hot spots" of the action. The fermionic eigenmodes show a high degree of local chirality. The lowest modes are seen to be localized in low-dimensional space-time regions.Comment: 13 pages, 11 figures, accepted to appear in the Proceedings of "HLRB, KONWIHR and Linux-Cluster: Review, Results and Future Projects Workshop", Leibniz Rechenzentrum Munich, December 200

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"Equation missing" -Odd Fluctuations in Heavy Ion Collisions. Deformed QCD as a Toy Model

Zhitnitsky

2013

Strongly Interacting Matter in Magnetic Fields

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Low-dimensional long-range topological charge structure in the QCD vacuum

Abstract: Low-dimensional long-range topological charge structure in the QCD vacuum Physical

Cited by 100 publications

References 30 publications

Locality and efficient evaluation of lattice composite fields: Overlap-based gauge operators

Locality and efficient evaluation of lattice composite fields: Overlap-based gauge operators

Topological Structure of the QCD Vacuum Revealed by Overlap Fermions

"Equation missing" -Odd Fluctuations in Heavy Ion Collisions. Deformed QCD as a Toy Model

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