Realization of all-to-all fermion propagator for the first principle high accuracy strong interaction prediction

TL;DR

The paper introduces a novel 'blending' algorithm that efficiently computes all-to-all fermion propagators, enabling high-accuracy calculations of multi-point correlation functions in quantum field theories like QCD.

Contribution

It presents a new blending algorithm combining low- and high-frequency modes for all-to-all fermion propagator estimation, improving the calculation of correlation functions in strongly interacting QFTs.

Findings

Successfully computed nucleon axial charges with high precision.

Validated the approach through consistency checks of pion form factors.

Demonstrated efficiency on 40 configurations at specified parameters.

Abstract

We propose a ``blending" algorithm that projects the all-to-all fermion propagator onto spatial low-frequency modes (LFM) combined with a stochastic estimate of spatial high-frequency modes (SHFM) at each time slice. This approach enables the calculation of arbitrary-point correlation functions for arbitrary hadron states in strongly interacting quantum field theories (QFT) with fermions, such as quantum chromodynamics (QCD). Specifically, LFM allows the construction of spatially extended hadron states below a certain energy threshold by diagonalizing multi-fermion interpolation fields. Meanwhile, the local interactions required for N-point correlation functions in QFT can be approximated in an unbiased manner through a reweighted summation of both LFM and SHFM contributions. To demonstrate the efficiency of this algorithm, we obtained {\color{black} $g_A^u=0.895(15)$, $g_A^d=-0.338(15)$, $g_A^s=-0.0245(72)$, $g_A^{u+d+s}=0.533(28)$ and $g_A^{u-d}=1.2339(43)$ } for nucleon at $m_{\pi}=300$ MeV and $a=0.077$ fm using 40 configurations. The consistency check of the pion electric form factor and charge radius derived from 3-point and 4-point correlation functions is also provided.