Graph Neural Networks in the Wilson Loop Representation of Abelian Lattice Gauge Theories
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 s...
| Authors | Ali Rayat, Gia-Wei Chern |
|---|---|
| Primary category | cond-mat.str-el |
| Published | 5 May 2026 |
| Last updated at source | 5 May 2026 |
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