质疑机器学习发现的自旋液体新态，指出其能量偏低是采样缺陷所致。
Comment on "Spin-1/2 Kagome Heisenberg Antiferromagnet: Machine Learning Discovery of the Spinon Pair-Density-Wave Ground State"
- 用自旋交换更新强制遍历采样，验证了原方法的采样偏差
- 在最大体系（N=108）上，修正后能量显著高于现有DMRG结果
- 适用于研究量子自旋系统中机器学习采样误差的读者
近期一篇论文（Phys. Rev. X 15, 011047 (2025)）利用群等变卷积神经网络研究了凯库勒自旋-1/2反铁磁海森堡模型的基态。在迄今最大的有限尺寸体系（N=108）上，作者报告的变分能量显著低于其他数值方法，包括最先进的密度矩阵重整化群（DMRG）计算结果。与以往可能为自旋液体基态的结论相反，作者观察到自旋子对密度波基态。我们发现：(i) 报告的低能量是马尔可夫链因单自旋翻转更新规则导致的非遍历性采样所造成的伪影；(ii) 当通过自旋交换更新强制实现遍历采样时，神经网络收敛到的能量显著高于现有DMRG结果，使该论文的主张受到质疑。
原文摘要 · Abstract (English)
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.
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