Gauge-equivariant graph neural networks embed non-Abelian local symmetries directly into message passing for lattice gauge theories, enabling learning of nonlocal observables from local operations.
Wen, Quantum orders and symmetric spin liquids, Physical Review B65, 165113 (2002)
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A gauge-invariant GNN using Wilson loops as inputs accurately predicts observables and simulates dynamics in Z2 and U(1) lattice gauge models.
Dipolar spin ice monopoles acquire finite magnetic charge from long-range dipole-dipole interactions via the dumbbell picture even classically, while octupolar spin ice monopoles have zero charge, providing a classical distinction between symmetry-enriched topological orders.
citing papers explorer
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Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theories
Gauge-equivariant graph neural networks embed non-Abelian local symmetries directly into message passing for lattice gauge theories, enabling learning of nonlocal observables from local operations.
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Graph Neural Networks in the Wilson Loop Representation of Abelian Lattice Gauge Theories
A gauge-invariant GNN using Wilson loops as inputs accurately predicts observables and simulates dynamics in Z2 and U(1) lattice gauge models.
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Classical symmetry enriched topological orders and distinct monopole charges for dipole-octupole spin ices
Dipolar spin ice monopoles acquire finite magnetic charge from long-range dipole-dipole interactions via the dumbbell picture even classically, while octupolar spin ice monopoles have zero charge, providing a classical distinction between symmetry-enriched topological orders.