Abstract:Local gauge structures play a central role in a wide range of condensed matter systems and synthetic quantum platforms, where they emerge as effective descriptions of strongly correlated phases and engineered dynamics. We introduce a gauge-invariant graph neural network (GNN) architecture for Abelian lattice gauge models, in which symmetry is enforced explicitly through local gauge-invariant inputs, such as Wilson loops, and preserved throughout message passing, eliminating redundant gauge degrees of freedom while retaining expressive power. We benchmark the approach on both $\mathbb{Z}_2$ and $\mathrm{U}(1)$ lattice gauge models, achieving accurate predictions of global observables and spatially resolved quantities despite the nonlocal correlations induced by gauge-matter coupling. We further demonstrate that the learned model serves as an efficient surrogate for semiclassical dynamics in $\mathrm{U}(1)$ quantum link models, enabling stable and scalable time evolution without repeated fermionic diagonalization, while faithfully reproducing both local dynamics and statistical correlations. These results establish gauge-invariant message passing as a compact and physically grounded framework for learning and simulating Abelian lattice gauge systems.
| Comments: | 13 pages, 6 figures |
| Subjects: | Strongly Correlated Electrons (cond-mat.str-el); Machine Learning (cs.LG); High Energy Physics - Lattice (hep-lat); Quantum Physics (quant-ph) |
| Cite as: | arXiv:2605.03901 [cond-mat.str-el] |
| (or arXiv:2605.03901v1 [cond-mat.str-el] for this version) | |
| https://doi.org/10.48550/arXiv.2605.03901 arXiv-issued DOI via DataCite (pending registration) |
From: Gia-Wei Chern [view email]
[v1]
Tue, 5 May 2026 15:55:21 UTC (6,640 KB)
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