Efficient Implementation of the Overlap Operator on Multi-GPUs

Alexandru, Andrei; Lujan, Michael; Pelissier, Craig; Gamari, Ben; Lee, Frank

doi:10.1109/saahpc.2011.13

Cited by 31 publications

(26 citation statements)

References 17 publications

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“…Implicitly restarted Arnoldi method [32,33] was used to compute the eigenvalues and eigenvectors of the overlap operator. For all but one ensemble used in this study, it is efficient to first compute the eigenvalues of D † D in a chiral sector, and then reconstruct the eigenvalues of D using standard techniques [34]. For the N = 64 pgQCD lattice at T = 1.12T c , it becomes problematic to distinguish the eigenvalues of near-zero eigenmodes from those of exact zero modes.…”

Section: Appendix B: Scale Invariance and Dirac Spectral Densitymentioning

confidence: 99%

Possible new phase of thermal QCD

Alexandru

Horváth

2019

Phys. Rev. D

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Using lattice simulations, we show that there is a phase of thermal QCD, where the spectral density ρ(λ) of Dirac operator changes as 1/λ for infrared eigenvalues λ < T .This behavior persists over the entire low energy band we can resolve accurately, over three orders of magnitude on our largest volumes. We propose that in this "IR phase", the well-known non-interacting scale invariance at very short distances (UV, λ → ∞, asymptotic freedom), coexists with very different interacting type of scale invariance at long distances (IR, λ < T ). Such dynamics may be responsible for the unusual fluidity properties of the medium observed at RHIC and LHC. We point out its connection to the physics of Banks-Zaks fixed point, leading to the possibility of massless glueballs in the fluid. Our results lead to the classification of thermal QCD phases in terms of IR scale invariance. The ensuing picture naturally subsumes the standard chiral crossover feature at "T c " ≈ 155 MeV. Its crucial new aspect is the existence of temperature T IR (200 MeV < T IR < 250 MeV) marking the onset of IR phase and possibly a true phase transition. arXiv:1906.08047v1 [hep-lat] 17 Jun 2019 1. Introduction. The study of strongly interacting matter as a function of temperature and baryon density is an active area of theoretical and experimental research (see [1] for recent review). At high energies of colliding heavy nuclei, such as those studied at LHC and the high end of RHIC, baryon densities are small enough so that the results are generally expected, among other things, to shed light on the nature and properties of thermal QCD transition in the early universe. In this regime, it has become widely accepted, largely due to the matured power of lattice QCD [2], that increasing temperature leads to a smooth crossover in properties of thermal strongly interacting matter. On the experimental side, results from RHIC [3-6] and LHC [7] based on modeling the time evolution of collisions in terms of relativistic hydrodynamics, produced a picture of strongly coupled liquid-like medium with extremely low η/s (shear viscosity/entropy density) at high temperatures. In parallel and initially independent developments, similar values of η/s were obtained in highly symmetric and strongly coupled gauge theories with large number of colors, studied by means of their holographic dual [8]. This sparked a flurry of attempts to model the medium seen in the experiments via more refined descriptions of this type.However, the physics of thermal QCD transition(s) and the nature of the discovered liquid-like state of matter are far from settled, even in the limit of vanishing net baryon density (µ = 0), the setting of our interest. Among other things, the currently favored scenario involving a single feature (crossover at"T c ") offers limited room for accommodating a dramatic change from medium described as weakly interacting hadron resonance gas to strongly interacting near-perfect fluid. In this work, we propose a hierarchy of thermal effects in QCD, based on scale inv...

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Section: Appendix B: Scale Invariance and Dirac Spectral Densitymentioning

confidence: 99%

Possible new phase of thermal QCD

Alexandru

Horváth

2019

Phys. Rev. D

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“…Compared to the earlier implementation of the overlap operator [20], the current implementation further improves the performance of data exchange on different nodes of the cluster and uses the polynomial approximation for the overlap operator instead of the rational approximation, and has achieved better scaling and further speed up of the calculation by a factor of two on average [21].…”

Section: Numerical Detailsmentioning

confidence: 99%

Stochastic method with low mode substitution for nucleon isovector matrix elements

et al. 2016

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We introduce a stochastic method with low-mode substitution to evaluate the connected threepoint functions. The isovector matrix elements of the nucleon for the axial-vector coupling g 3 A , scalar couplings g 3 S and the quark momentum fraction x u−d are calculated with overlap fermion on 2+1 flavor domain-wall configurations on a 24 3 ×64 lattice at mπ = 330 MeV with lattice spacing a = 0.114 fm.

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“…For neutral particles in a constant electric field the correlation functions still retain their single exponential decay in the limit t → ∞. In particular we have 5) where E(E ) has the perturbative expansion in the electric field given by Table 1). The right panel is the same plot but with the values ofdγ 5 d scaled by a factor of 4.…”

Section: Introductionmentioning

confidence: 92%

“…For the E 220 ensemble we used similar values: m π = 270, 300, 340 and 370 MeV. To increase our efficiency of quark propagator calculations we used an optimally implemented multi-GPU Dslash operator [5], along with an efficient BiCGstab multi-mass inverter [6].…”

Section: Pos(lattice 2013)287mentioning

confidence: 99%

Electric Polarizability of hadrons with nHYP-Clover fermions

Lujan¹,

Alexandru²,

Freeman³

et al. 2014

Proceedings of 31st International Symposium on Lattice Field Theory LATTICE 2013 — PoS(LATTICE 2013)

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We present preliminary calculations for the electric polarizability of the neutral pion and neutron on three dynamically generated nHYP-Clover ensembles. We use two different pion masses (m π 300 and 220 MeV) to gauge the chiral behavior. The effects of partial quenching are analyzed by computing a string of partial quenched valence masses for each ensemble. We also analyzed the volume dependence using elongated lattices, where the elongation is in the direction of the electric field.

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Efficient Implementation of the Overlap Operator on Multi-GPUs

Cited by 31 publications

References 17 publications

Possible new phase of thermal QCD

Possible new phase of thermal QCD

Stochastic method with low mode substitution for nucleon isovector matrix elements

Electric Polarizability of hadrons with nHYP-Clover fermions

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