Graph Neural Networks in the Wilson Loop Representation of Abelian Lattice Gauge Theories

• URL: http://arxiv.org/abs/2605.03901v1
• Date: Tue, 05 May 2026 15:55:21 GMT
• Title: Graph Neural Networks in the Wilson Loop Representation of Abelian Lattice Gauge Theories
• Abstract summary: Local gauge structures play a central role in a wide range of condensed matter systems and synthetic quantum platforms.<n>We introduce a gauge-invariant graph neural network architecture for Abelian lattice gauge models.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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