Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
This addresses the computational bottleneck of topological freezing in lattice QCD simulations for physicists, offering an incremental improvement over existing methods.
The paper tackles the problem of topological freezing in lattice gauge theories by developing a methodology that combines open boundary conditions with a non-equilibrium Monte Carlo approach to efficiently sample topology, achieving full control of scaling at lattice spacings as small as 0.045 fm and showing superior performance with a customized Stochastic Normalizing Flow.
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.