Multilevel Plaquette-Space Sampling for Lattice Gauge Theories with Local Constraint Solves
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.
Related
- Sector-Resolved Flow Sampling for Topologically Frozen Lattice Gauge Theories
- AT-SKM-Net: An Accelerated Trainable Sampling Kaczmarz-Motzkin Framework for Linear Hard-Constraint Feasibility on Dynamic Graphs
- Fourier sampling on a lattice
- Super-Arrhenius relaxation of the triangular plaquette model in any dimension
- Multilevel limits of spiked random matrix corners processes
BibTeX
@misc{singha2026multilevel,
title = {{Multilevel Plaquette-Space Sampling for Lattice Gauge Theories with Local Constraint Solves}},
author = {Ankur Singha and Jacob Finkenrath and Karl Jansen and Vipul Arora and Shinichi Nakajima},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35722},
eprint = {2609.35722},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35722},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Multilevel Plaquette-Space Sampling for Lattice Gauge Theories with Local Constraint Solves
AU - Ankur Singha
AU - Jacob Finkenrath
AU - Karl Jansen
AU - Vipul Arora
AU - Shinichi Nakajima
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35722
UR - https://arxiv.org/abs/2609.35722
AB - 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.
ER -