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

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Rayat, Ali, Chern, Gia-Wei
Natura: Preprint
Pubblicazione: 2026
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866909014644752384
author Rayat, Ali
Chern, Gia-Wei
author_facet Rayat, Ali
Chern, Gia-Wei
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2605_03901
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Graph Neural Networks in the Wilson Loop Representation of Abelian Lattice Gauge Theories
Rayat, Ali
Chern, Gia-Wei
Strongly Correlated Electrons
Machine Learning
High Energy Physics - Lattice
Quantum Physics
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.
title Graph Neural Networks in the Wilson Loop Representation of Abelian Lattice Gauge Theories
topic Strongly Correlated Electrons
Machine Learning
High Energy Physics - Lattice
Quantum Physics
url https://arxiv.org/abs/2605.03901