发表机构
QudeLeap Research; The Hong Kong University of Science and Technology (Guangzhou)（酷跃研究; 香港科技大学（广州））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出Complex Psiformer，在复空间中结合注意力机制优化磁性多电子波函数，在多个基准上优于实部模型，为有限磁性系统能量与电荷研究提供有效变分方法。
AI 中文摘要
磁性多电子波函数需要振幅和相位同时优化。复内部表示是否能改善这种变分搜索，是神经波函数设计中的一个实际问题。我们针对磁性莫尔连续体中的相互作用电子引入了Complex Psiformer，将复隐特征和厄米幅度注意力与磁性边界条件及费米子反对称性相结合。在相同数量的优化步骤后，Complex Psiformer在两个有限超胞中达到比Real Psiformer更低的能量。两种Psiformer也分别优于其对应的神经Hartree-Fock参考。在25胞系统中，跨越五个训练种子的平均Complex优势为每电子1.458 meV，且观测到的离散度更小。单独训练的双电子Complex态与有限组态相互作用参考之间的能隙小于其Real对应态。在Complex态中，通量扫描显示非单调的密度关联和在高通量下较弱的蜂窝平均密度调制，而连通涨落持续存在。规范不变电流图提供了优化态中局部环流的定性比较。这些基准支持组合架构作为研究有限磁性系统中能量和电荷排列的变分拟设。
英文摘要
Magnetic many-electron wavefunctions require amplitude and phase to be optimized together. Whether a complex internal representation improves this variational search is a practical question for neural wavefunction design. We introduce Complex Psiformer for interacting electrons in a magnetic moiré continuum, combining complex hidden features and Hermitian-magnitude attention with magnetic boundary conditions and fermionic antisymmetry. After the same number of optimization steps, Complex Psiformer reaches lower energies than Real Psiformer in two finite supercells. Both Psiformers also improve on their respective neural Hartree-Fock references. Across five training seeds in the 25-cell system, the mean Complex advantage is 1.458 meV per electron, with a smaller observed spread. A separately trained two-electron Complex state has a smaller energy gap to a finite configuration interaction reference than its Real counterpart. In the Complex states, flux scans show nonmonotonic density correlations and weaker honeycomb mean-density modulation at higher flux, while connected fluctuations persist. Gauge invariant current maps provide a qualitative comparison of local circulation in the optimized states. These benchmarks support the combined architecture as a variational ansatz for studying energies and charge arrangements in finite magnetic systems.
Comments24 pages, 11 figures, GitHub repo: https://github.com/QuAIR/ComplexPsiformer
