Physics-Conditioned Diffusion Models for Lattice Gauge Theory
This provides a novel computational method for physicists studying quantum field theories, offering potential efficiency gains over traditional algorithms.
The authors developed diffusion models incorporating stochastic quantization to simulate lattice gauge theories, demonstrating successful extrapolation to larger inverse coupling regions without topological freezing and enabling sampling on different lattice sizes without retraining.
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.