Evidence for a Dirac Spin Liquid in the Kagome Heisenberg Antiferromagnet from High-Precision Neural-Network Quantum States
Abstract
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 Z2 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.
Related
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- Theory of the 1/9 Magnetization Plateau of the Spin-1/2 Kagome Heisenberg Antiferromagnet
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BibTeX
@misc{sun2026evidence,
title = {{Evidence for a Dirac Spin Liquid in the Kagome Heisenberg Antiferromagnet from High-Precision Neural-Network Quantum States}},
author = {Zheng-Hang Sun and Christopher Roth and Ao Chen and Markus Heyl},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05174},
eprint = {2611.05174},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05174},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Evidence for a Dirac Spin Liquid in the Kagome Heisenberg Antiferromagnet from High-Precision Neural-Network Quantum States
AU - Zheng-Hang Sun
AU - Christopher Roth
AU - Ao Chen
AU - Markus Heyl
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05174
UR - https://arxiv.org/abs/2611.05174
AB - 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.
ER -