ETD

• critical slowing down
• generative models
• lattice gauge theory
• normalizing flows
• spectral refinement

Many fundamental physical theories are gauge theories, built upon Lagrangians invariant under local Lie-group symmetries; a prominent example is the Standard Model of particle physics. Since the perturbative formulation is not viable at strong coupling, numerical simulations remain the only practicable approach to compute quantities of interest from first principles, typically relying on Markov chain Monte Carlo methods.
Despite their robustness, these methods face severe efficiency bottlenecks. As the system approaches a second-order transition or the continuum limit, critical slowing down emerges and the autocorrelation time diverges, raising the computational cost. In theories with topological sectors, it manifests as topological freezing: the algorithm remains trapped within a single value of the topological charge, preventing ergodic sampling. Several methods have been proposed to address this, yet the problem remains open. In this sense, normalizing flows have recently emerged as a promising alternative, offering a fundamentally different sampling strategy.
This work analyzes their implementation by simulating fermion-free Quantum Electrodynamics in 1+1 dimensions. The approach is tested thoroughly, studying its scaling with the lattice volume and pushing it towards highly critical regimes to expose the bottlenecks of the current implementation. Building on these results, a novel refinement scheme is then proposed: working in momentum space, it removes the frequency values that are an artifact of the lattice formulation and uses the refined configuration, obtained through an additional CNN, to find better mapping parameters.