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We study the performance of all-mode-averaging (AMA) when used in conjunctionwith a locally deflated SAP-preconditioned solver, determining how to optimizethe local block sizes and number of deflation fields in order to minimize thecomputational cost for a given level of overall statistical accuracy. We findthat AMA enables a reduction of the statistical error on nucleon charges by afactor of around two at the same cost when compared to the standard method. Asa demonstration, we compute the axial, scalar and tensor charges of the nucleonin $N_f=2$ lattice QCD with non-perturbatively O(a)-improved Wilson quarks,using O(10,000) measurements to pursue the signal out to source-sinkseparations of $t_s\sim 1.5$ fm. Our results suggest that the axial charge issuffering from a significant amount (5-10%) of excited-state contamination atsource-sink separations of up to $t_s\sim 1.2$ fm, whereas the excited-statecontamination in the scalar and tensor charges seems to be small.

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