Variance reduction in lattice QCD observables via normalizing flows

TL;DR

This paper demonstrates how normalizing flows can significantly reduce variance in lattice QCD observable estimations, improving computational efficiency in gauge theories like SU(3) Yang-Mills and QCD.

Contribution

It introduces a novel application of normalizing flows for variance reduction in lattice gauge theory observables involving gluonic operators.

Findings

Achieved variance reduction factors of 10-60 in glueball correlators.

Variance reduction is approximately volume-independent, enabling cost-effective training.

Demonstrated computational advantages in QCD and Yang-Mills simulations.

Abstract

Normalizing flows can be used to construct unbiased, reduced-variance estimators for lattice field theory observables that are defined by a derivative with respect to action parameters. This work implements the approach for observables involving gluonic operator insertions in the SU(3) Yang-Mills theory and two-flavor Quantum Chromodynamics (QCD) in four space-time dimensions. Variance reduction by factors of $10$-$60$ is achieved in glueball correlation functions and in gluonic matrix elements related to hadron structure, with demonstrated computational advantages. The observed variance reduction is found to be approximately independent of the lattice volume, so that volume transfer can be utilized to minimize training costs.