快速、准确且可扩展的费米子神经网络：基于平移等变性
Fast, Accurate, and Scalable Fermionic Neural Networks via Translation Equivariance
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中文总结 AI 辅助
本文提出TorFormer，一种基于平移等变性的费米子神经网络，通过精确满足哈密顿量对称性，显著提升训练速度和能量精度，高效解决大规模量子多体问题。
中文摘要 AI 辅助
我们证明，将神经量子态设计为哈密顿量对称性的精确本征态，能显著提升训练速度和最终变分能量。针对二维电子气，我们设计了TorFormer，一种作为总动量精确本征态的神经网络波函数。TorFormer无需监督即可描述费米液体和维格纳晶体，并在大系统尺寸下显著优于基于Psiformer的参考模型。在$N=91$时，对于$r_s = 30.0$和$40.0$，我们将TorFormer训练$8\mathrm{K}$步的结果与先前最佳NQS（需$100\mathrm{K}$训练步）进行比较。在$r_s = 40.0$时，排除平凡的Madelung部分，我们对总能量的改进为$0.12\\%$——与相间微小差异相比，这一改进巨大。相对于Slater-Jastrow-backflow扩散蒙特卡洛，TorFormer的能量降低约为先前最佳NQS的$9.8$倍。我们的工作表明，神经量子态既能准确又能高效地解决大规模问题。
英文摘要
We demonstrate that designing a neural quantum state to be an exact eigenstate of the Hamiltonian's symmetries significantly improves both training speed and final variational energy. For the 2D electron gas, we design TorFormer, a neural network wavefunction which is an exact eigenstate of the total momentum. TorFormer describes both the Fermi liquid and Wigner crystal with no supervision and significantly outperforms Psiformer-based references up to large system sizes. For $r_s = 30.0$ and $40.0$ at $N=91$, we compare TorFormer trained for $8\mathrm{K}$ steps against the previous best NQS, which required $100\mathrm{K}$ training steps. Our improvement to the total energy at $r_s = 40.0$, excluding the trivial Madelung part, is $0.12\%$---enormous compared to the tiny differences separating phases. Relative to Slater-Jastrow-backflow diffusion Monte Carlo, TorFormer's energy decrease is roughly $9.8$ times that of the previous best NQS. Our work demonstrates that neural quantum states can both accurately and efficiently solve large-scale problems.
发表机构
- Massachusetts Institute of Technology（麻省理工学院）
- Taiwan Semiconductor Manufacturing Company（台湾半导体制造公司）
机构由 AI 辅助整理，请以论文原文为准。
