Covariant approximation averaging

Abstract

We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in N f = 2 + 1 lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.

Hadron Structure

“…For the case of g A a speed up of ∼ 5-20 times is reported using N f =2+1 DWF configurations on a 24 3 × 48 lattice, and up to 10-30 times for a larger lattice, 32 3 × 64 [31].…”

“…Thus, noice reduction methods are highly valuable. RBC/UKQCD has implemented a new class of covariant approximation averaging techniques, called All-Mode-Averaging (AMA) [31] which allows for a significant decrease of the statistical error over conventional methods at reduced computational cost. The AMA technique achieves an increase of the number of measurement, N meas , at a low computational cost, by constructing an improved operator which is built from a low-precision and thus cheap part, and a correction term, to compensate the bias introduced by the approximate measurements:…”

Neutron and proton electric dipole moments fromNf=2+1domain-wall fermion lattice QCD

“…Quark propagators are computed using the conjugate gradient (CG) algorithm and the 4D-even-odd-preconditioned Dirac operator [48][49][50]. As shown in Tab.…”

“…To pursue a more reliable estimate of the neutron and proton EDM's, we adopt strategy (2) and use DWF. To efficiently reduce statistical errors we employ all-mode-averaging (AMA) [48][49][50].…”

A precise determination of the HVP contribution to the muon anomalous magnetic moment from lattice QCD

“…The precision degradation at long distances is clearly visible. We employ a multi-step approximation scheme with low-mode averaging [7] over the entire volume and two levels of approximations in a stopped deflated solver (AMA) [8][9][10][11] of randomly positioned point sources. Figure 3 contrasts the statistical precision of this improved estimator with the traditional choice of Z 2 wall sources and we observe a reduction of noise by one order of magnitude at same cost.…”