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.

47 pages, 17 figures, reference added and minor revision, v2: added figure, published version

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• Lattice Calculation of Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment
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• The anomalous magnetic moment of the muon: status of Lattice QCD calculations
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• Nucleon Sigma Terms with $N_f=2+1$ O($a$)-improved Wilson fermions
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• Lattice QCD Calculation of $x$-dependent Meson Distribution Amplitudes at Physical Pion Mass with Threshold Logarithm Resummation
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• Emergence of the $\rho$ resonance from the HAL QCD potential in lattice QCD
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