2017
DOI: 10.2172/1422713
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Disconnected Diagrams in Lattice QCD

Abstract: In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called "disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rig… Show more

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Cited by 1 publication
(3 citation statements)
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“…where we have taken into account that the Frobenius norm, for some matrix 𝐴, obeys ‖𝐴‖ 𝐹 = ‖𝐴 𝑇 ‖ 𝐹 , and ‖𝑈𝐴‖ 𝐹 = ‖𝐴‖ 𝐹 if 𝑈 is unitary. Equations ( 6) and (7) give us a clear indication that the variance of the Hutchinson estimator, when applied to the problem posed in Equation (1), is proportional to the sum of the inverses of the smallest singular values of 𝐷 plus the term Re(tr( P𝐷 −𝐻 P𝐷 −𝑇 )). For the same matrix used in Figure 1, we have evaluated 𝐷 −𝐻 𝐷 −𝑇 and P𝐷 −𝐻 P𝐷 −𝑇 and present the results in Figure 2.…”
Section: Variances In the Hutchinson Methodsmentioning
confidence: 99%
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“…where we have taken into account that the Frobenius norm, for some matrix 𝐴, obeys ‖𝐴‖ 𝐹 = ‖𝐴 𝑇 ‖ 𝐹 , and ‖𝑈𝐴‖ 𝐹 = ‖𝐴‖ 𝐹 if 𝑈 is unitary. Equations ( 6) and (7) give us a clear indication that the variance of the Hutchinson estimator, when applied to the problem posed in Equation (1), is proportional to the sum of the inverses of the smallest singular values of 𝐷 plus the term Re(tr( P𝐷 −𝐻 P𝐷 −𝑇 )). For the same matrix used in Figure 1, we have evaluated 𝐷 −𝐻 𝐷 −𝑇 and P𝐷 −𝐻 P𝐷 −𝑇 and present the results in Figure 2.…”
Section: Variances In the Hutchinson Methodsmentioning
confidence: 99%
“…In lattice quantum chromodynamics (lattice QCD), the extraction of some observables requires the computation of matrix traces [1] of the form trfalse(ffalse(Dfalse)false)$\mathrm{tr}(f(D))$ with D the Dirac operator on the lattice, and f(D)=false(normalΓDfalse)1$f(D) = (\Gamma D)^{-1}$ with Γ some Dirac structure, for example, normalΓ=Γ5$\Gamma = \Gamma _{5}$. This appears, for example, in the calculation of disconnected diagrams [1]. Furthermore, in the context of generalized parton distributions [2], the computation of off‐diagonal elements of D1$D^{-1}$, stemming from a displacement along one of the four spacetime dimensions on the lattice, is required; this problem can be reformulated as computing the trace trfalse(D1PHfalse)$\mathrm{tr}(D^{-1} \widetilde{P}^{H})$, with P$\widetilde{P}$ the permutation matrix resulting from the displacement on the lattice.…”
Section: Introductionmentioning
confidence: 99%
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