Multiscale Monte Carlo equilibration: Pure Yang-Mills theory

TL;DR

This paper introduces a multiscale Monte Carlo algorithm for pure Yang-Mills theory that improves the efficiency of generating uncorrelated gauge configurations and mitigates topological freezing.

Contribution

It combines Monte Carlo methods with renormalization group and multigrid ideas to enhance lattice gauge theory simulations.

Findings

Efficient parallel generation of gauge configurations.

Reduces topological freezing at small lattice spacings.

Applicable to heat bath and hybrid Monte Carlo methods.

Abstract

We present a multiscale thermalization algorithm for lattice gauge theory, which enables efficient parallel generation of uncorrelated gauge field configurations. The algorithm combines standard Monte Carlo techniques with ideas drawn from real space renormalization group and multigrid methods. We demonstrate the viability of the algorithm for pure Yang-Mills gauge theory for both heat bath and hybrid Monte Carlo evolution, and show that it ameliorates the problem of topological freezing up to controllable lattice spacing artifacts.