Generalizable Equivariant Diffusion Models for Non-Abelian Lattice Gauge Theory

We demonstrate that gauge equivariant diffusion models can accurately model the physics of non-Abelian lattice gauge theory using the Metropolis-adjusted annealed Langevin algorithm (MAALA), as exemplified by computations in two-dimensional U(2) and SU(2) gauge theories. Our network architecture is based on lattice gauge equivariant convolutional neural networks (L-CNNs), which respect local and global symmetries on the lattice. Models are trained on a single ensemble generated using a traditional Monte Carlo method. By studying Wilson loops of various size as well as the topological susceptibility, we find that the diffusion approach generalizes remarkably well to larger inverse couplings and lattice sizes with negligible loss of accuracy while retaining moderately high acceptance rates.

Physics-Conditioned Diffusion Models for Lattice Gauge Theory

We develop diffusion models for simulating lattice gauge theories, where stochastic quantization is explicitly incorporated as a physical condition for sampling. We demonstrate the applicability of this novel sampler to U(1) gauge theory in two spacetime dimensions and find that a model trained at a small inverse coupling constant can be extrapolated to larger inverse coupling regions without encountering the topological freezing problem. Additionally, the trained model can be employed to sample configurations on different lattice sizes without requiring further training. The exactness of the generated samples is ensured by incorporating Metropolis-adjusted Langevin dynamics into the generation process. Furthermore, we demonstrate that this approach enables more efficient sampling of topological quantities compared to traditional algorithms such as Hybrid Monte Carlo and Langevin simulations.