Nucleon matrix elements from lattice QCD with all-mode-averaging and a domain-decomposed solver: An exploratory study
Georg von Hippel (PRISMA Cluster of Excellence, Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, Mainz, D-55099, Germany)
; Thomas D. Rae (Bergische Universität Wuppertal, Gaußstraße 20, Wuppertal, D-42119, Germany); Eigo Shintani (PRISMA Cluster of Excellence, Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, Mainz, D-55099, Germany, RIKEN Advanced Institute for Computational Science, Kōbe, Hyōgo, 650-0047, Japan); Hartmut Wittig (PRISMA Cluster of Excellence, Institut für Kernphysik, Johannes Gutenberg-Universität Mainz, Mainz, D-55099, Germany, Helmholtz Institute Mainz, University of Mainz, Mainz, 55099, Germany)
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 Nf=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 tsâ¼1.5Â fm . Our results suggest that the axial charge is suffering from a significant amount (5â10%) of excited-state contamination at source-sink separations of up to tsâ¼1.2Â fm , whereas the excited-state contamination in the scalar and tensor charges seems to be small.
