Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory

TL;DR

This paper introduces a novel non-equilibrium Monte Carlo method combined with flow-based techniques to efficiently sample topological sectors in lattice gauge theories, especially near the continuum limit.

Contribution

It develops a new methodology using out-of-equilibrium simulations and flow-based models to mitigate topological freezing in SU(3) gauge theory.

Findings

Reduced autocorrelation of topological charge with open boundary conditions.

Achieved efficient topology sampling at lattice spacings as small as 0.045 fm.

Designed a customized Stochastic Normalizing Flow outperforming traditional methods.

Abstract

We develop a methodology based on out-of-equilibrium simulations to mitigate topological freezing when approaching the continuum limit of lattice gauge theories. We reduce the autocorrelation of the topological charge employing open boundary conditions, while removing exactly their unphysical effects using a non-equilibrium Monte Carlo approach in which periodic boundary conditions are gradually switched on. We perform a detailed analysis of the computational costs of this strategy in the case of the four-dimensional $\mathrm{SU}(3)$ Yang-Mills theory. After achieving full control of the scaling, we outline a clear strategy to sample topology efficiently in the continuum limit, which we check at lattice spacings as small as $0.045$ fm. We also generalize this approach by designing a customized Stochastic Normalizing Flow for evolutions in the boundary conditions, obtaining superior performances with respect to the purely stochastic non-equilibrium approach, and paving the way for more efficient future flow-based solutions.