Nucleon matrix elements from lattice QCD with all-mode-averaging and a domain-decomposed solver: An exploratory study

Abstract

We study the performance of all-mode-averaging (AMA) when used in conjunction with a locally deflated SAP-preconditioned solver, determining how to optimize the local block sizes and number of deflation fields in order to minimize the computational cost for a given level of overall statistical accuracy. We find that AMA enables a reduction of the statistical error on nucleon charges by a factor of around two at the same cost when compared to the standard method. As a demonstration, we compute the axial, scalar and tensor charges of the nucleon in N f = 2 lattice QCD with non-perturbatively O(a)-improved Wilson quarks, using O(10,000) measurements to pursue the signal out to source-sink separations of t s ∼ 1.5 fm. Our results suggest that the axial charge is suffering from a significant amount (5-10%) of excited-state contamination at source-sink separations of up to t s ∼ 1.2 fm, whereas the excited-state contamination in the scalar and tensor charges seems to be small.

Nucleon form factors and root-mean-square radii on a (10.8 fm)4 lattice at the physical point

“…N org and N G are the number of such a transformed observable for O (org) and O (approx) respectively. To achieve the high performance of AMA, we need to set N org ≪ N G satisfying the strong correlation r between O org and O (approx) , as 2(1 − r) < 1/N G [22,23]. Following Refs.…”

“…(10) and extracted from the ratio R 5z P (t, q) of Eq. (23). Figure 22 shows the t dependence of the ratio with |n| 2 = 1, 2, 3, 4 for t sep /a = 10, 12, 14, 16.…”

“…(iii) Using the variation of the source-sink separation as t sep /a = t sink /a−t src /a = 10, 12,14,16, where the largest one is about 1.35 fm, we can examine the possible excited state contributions, which has not been studied in the previous work [20], where a single choice of t sep /a = 15 was used. (iv) Significant reduction of the computational cost is possible to utilize the all-mode-averaging (AMA) method [21][22][23] optimized by the deflation technique [24]. This paper is organized as follows: Section II presents the definition of nucleon form factors to fix the notations in this paper.…”

Finite-volume correction on the hadronic vacuum polarization contribution to the muon g−2 in lattice QCD

“…(4) 3.9 187 0.126119 * 0.124902 0.1354(9) 0.4999 (4) 3.7 87 with covariant transformation g ∈ G under subset of its symmetry G. Here G corresponds to translational symmetry and its size is N G for approximation and N org for original. In [36], one of the authors have developed the highly optimized AMA using Schwartz Alternative Procedure (SAP) deflation preconditioning [48,49]. From a knowledge of tuning parameter to reduce the computational cost of approximation in AMA, SAP deflation makes an achievement of the high performance in the measurement on PACS configurations compared to low-mode deflation (see Appendix A).…”

“…In Table 2, we show the detail of parameters to generate approximation O (appx) in AMA on each gauge ensemble. In the computation of O AMA , we use a method with fixed number of iteration of General Conjugate Residual (GCR) solver with SAP deflation as used in [36]. In a generation of SAP deflation field, the domain block size, the number of SAP cycle n cy and the number of deflation vector are tuned as in Table 2.…”