# Comment on "Spin-1/2 Kagome Heisenberg Antiferromagnet: Machine Learning Discovery of the Spinon Pair-Density-Wave Ground State"

arXiv: https://arxiv.org/abs/2605.28861 · HTML: https://mlsanity.com/paper/2605.28861/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 0 of its 4 references that are in the map.
- First posted on arXiv 21 May 2026.

## Abstract (arXiv)

A recent article [Phys. Rev. X 15, 011047 (2025)] utilizes group-equivariant convolutional neural networks to study the ground state of the kagome Heisenberg antiferromagnet. On the largest finite-size cluster studied to date (N=108), the authors report variational energies significantly lower than other numerical methods, including state-of-the-art density matrix renormalization group (DMRG) calculations. In contrast to previous results suggesting a possible spin-liquid ground state, the authors observe a spinon pair-density-wave ground state. We find that: (i) the reported low energies are artifacts of broken ergodicity in the Metropolis--Hastings sampling, since the single-spin-flip update rule utilized by the authors effectively freezes the Markov chains; and (ii) when ergodic sampling is enforced via spin-exchange updates, the neural network converges to energies significantly higher than existing DMRG results, calling the paper's claims into question.