Multilevel Plaquette-Space Sampling for Lattice Gauge Theories with Local Constraint Solves
hep-lat, hep-th, math-ph, math.MP, quant-ph
Submitted: 2026-09-28
Updated: 2026-09-28
Comments: 9 pages main text, 38 pages total, 10 figures, 9 tables
License: http://creativecommons.org/licenses/by/4.0/
The gist: Lattice gauge theories are an important class of physical models with high-dimensional structured distributions that underpin first-principles calculations in particle, nuclear, and condensed-matter
Terminology
Abstract
Lattice gauge theories are an important class of physical models with high-dimensional structured distributions that underpin first-principles calculations in particle, nuclear, and condensed-matter physics. Recent advances in generative modeling have opened new avenues for sampling Boltzmann distributions in lattice gauge theories, offering the potential to alleviate limitations of traditional Monte Carlo methods, including critical slowing down and topological freezing. However, generative samplers for lattice gauge theories are typically constructed in link space, where correlations become increasingly long-ranged toward weak coupling, posing a challenge for learning. Plaquettes provide a more natural representation, as the action is local in these variables. However, exact Bianchi constraints restrict them to a lower-dimensional manifold, complicating direct generative modeling. We introduce a multilevel normalizing-flow construction that samples directly in plaquette space while satisfying these constraints exactly. The key idea is a coarse-to fine factorization that transforms a globally coupled constraint problem into a sequence of local solves: at each refinement, every determined plaquette depends on at most four newly generated variables, while the size of the constraint problem remains independent of the lattice size. We validate the construction for U(1) in two and four dimensions and for SU(2) in two dimensions. Our multilevel Plaquette-Space Sampler (PSS) substantially outperforms link-space baselines, with the advantage increasing toward weak coupling, where the gauge coupling becomes small. This regime is particularly challenging for generative sampling and, in asymptotically free gauge theories, is relevant to continuum studies.
Sources
- Generalizable Equivariant Diffusion Models for Non-Abelian Lattice Gauge Theory
- Variance reduction in lattice QCD observables via normalizing flows
- Learning the generating functional for variance reduction in lattice QCD
- Normalizing flows for lattice gauge theory in arbitrary space-time dimension
- Introduction to Normalizing Flows for Lattice Field Theory
- Sampling two-dimensional spin systems with transformers
- Variational Autoregressive Networks with probability priors
- A scalable flow-based approach to mitigate topological freezing
- Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
- Stochastic normalizing flows for lattice field theory
- Stochastic Path Sampler For Lattice Field Theory
- Renormalizing Diffusion Models
- Comparison of topology changing update algorithms
- Improvement of Heatbath Algorithm in LFT using Generative models
- Lattice gauge equivariant convolutional neural networks
- Flow-based sampling for multimodal and extended-mode distributions in lattice field theory
- Normalizing flows for all-orders QED corrections in lattice field theory
- Generative sampling with physics-informed kernels
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