A scalable flow-based approach to mitigate topological freezing

TL;DR

This paper introduces a scalable flow-based method using Stochastic Normalizing Flows to address topological freezing in lattice gauge theories, enabling efficient sampling of topological sectors without boundary artifacts.

Contribution

It presents a novel, exact flow-based technique that transports configurations from open boundary conditions to periodic ensembles, improving sampling efficiency in 4d SU(3) Yang--Mills theory.

Findings

The method effectively reduces autocorrelations in topological observables.

It outperforms purely stochastic methods at similar computational costs.

The approach accurately reproduces known topological susceptibility results.

Abstract

As lattice gauge theories with non-trivial topological features are driven towards the continuum limit, standard Markov Chain Monte Carlo simulations suffer for topological freezing, i.e., a dramatic growth of autocorrelations in topological observables. A widely used strategy is the adoption of Open Boundary Conditions (OBC), which restores ergodic sampling of topology but at the price of breaking translation invariance and introducing unphysical boundary artifacts. In this contribution we summarize a scalable, exact flow-based strategy to remove them by transporting configurations from a prior with a OBC defect to a fully periodic ensemble, and apply it to 4d SU(3) Yang--Mills theory. The method is based on a Stochastic Normalizing Flow (SNF) that alternates non-equilibrium Monte Carlo updates with localized, gauge-equivariant defect coupling layers implemented via masked parametric stout smearing. Training is performed by minimizing the average dissipated work, equivalent to a Kullback--Leibler divergence between forward and reverse non-equilibrium path measures, to achieve more reversible trajectories and improved efficiency. We discuss the scaling with the number of degrees of freedom affected by the defect and show that defect SNFs achieve better performances than purely stochastic non-equilibrium methods at comparable cost. Finally, we validate the approach by reproducing reference results for the topological susceptibility.