Application of Quadrature Methods for Re-Weighting in Lattice QCD

TL;DR

This paper explores the use of quadrature methods combined with noise vectors to compute determinant ratios in lattice QCD re-weighting, offering a potentially more efficient computational approach.

Contribution

It introduces a novel application of quadrature methods for determinant ratio computation in lattice QCD re-weighting, enabling separate calculations of determinants with improved bias control.

Findings

Quadrature methods can compute determinants separately for operators $\

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Bootstrap re-sampling reduces bias in determinant estimation.

Abstract

Re-weighting is a useful tool that has been employed in Lattice QCD in different contexts including, tuning the strange quark mass, approaching the light quark mass regime, and simulating electromagnetic fields on top of QCD gauge configurations. In case of re-weighting the sea quark mass, the re-weighting factor is given by the ratio of the determinants of two Dirac operators $D_a$ and $D_b$. A popular approach for computing this ratio is to use a pseudofermion representation of the determinant of the composite operator $\Omega=D_a(D_b^\dagger D_b)^{-1} D_a^\dagger$. Here, we study using quadrature methods together with noise vectors to compute the ratio of determinants. We show that, with quadrature methods each determinant can be computed separately using the operators $\Omega_a=D_a^\dagger D_a$ and $\Omega_b=D_b^\dagger D_b$. We also discuss using bootstrap re-sampling to remove the bias from the determinant estimator.