Evidence for a Dirac Spin Liquid in the Kagome Heisenberg Antiferromagnet from High-Precision Neural-Network Quantum States

The spin-1/2 kagome Heisenberg antiferromagnet is a central model in the study of quantum spin liquids, yet its ground-state properties remain unresolved. We perform large-scale variational Monte-Carlo calculations using neural-network quantum states (NQSs) with kagome-geometry-aware message-passing convolution on two-dimensional tori containing up to 300 spins, and achieve exceptionally low variational energies for the kagome model. The spin and dimer structure factors show no evidence of magnetic or valence-bond long-range order. Moreover, the dominant symmetry-resolved spin and dimer correlations exhibit a common scaling behavior consistent with the emergent $SO(6)$ monopole multiplet of the Dirac spin liquid. Finally, the fidelity of the optimized NQSs with Gutzwiller-projected mean-field states increasingly favors the Dirac state over the competing $Z_{2}$ candidates as the system size grows. Together, these complementary results provide evidence for a $U(1)$ Dirac spin-liquid ground state in the kagome Heisenberg antiferromagnet.