A multilevel algorithm for flow observables in gauge theories

TL;DR

This paper introduces a multilevel algorithm to efficiently compute flow observables in gauge theories, significantly improving convergence rates for correlation functions like topological charge and energy density.

Contribution

The authors propose a novel multilevel algorithm that enables faster Monte Carlo convergence for flow observable correlations in gauge theories.

Findings

Faster convergence of correlation functions using the multilevel approach

Successful demonstration with topological charge and energy density

Potential for improved computational efficiency in gauge theory simulations

Abstract

We study the possibility of using multilevel algorithms for the computation of correlation functions of gradient flow observables. For each point in the correlation function an approximate flow is defined which depends only on links in a subset of the lattice. Together with a local action this allows for independent updates and consequently a convergence of the Monte Carlo process faster than the inverse square root of the number of measurements. We demonstrate the feasibility of this idea in the correlation functions of the topological charge and the energy density.