Learning Quantum Matter through Attention in Complex Space
Abstract
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.
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BibTeX
@misc{jing2026learning,
title = {{Learning Quantum Matter through Attention in Complex Space}},
author = {Mingrui Jing and Erdong Huang and Jizhe Lai and Enji Xiong and Jin-Guo Liu and Xin Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11792},
eprint = {2609.11792},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11792},
}
RIS
TY - UNPB
TI - Learning Quantum Matter through Attention in Complex Space
AU - Mingrui Jing
AU - Erdong Huang
AU - Jizhe Lai
AU - Enji Xiong
AU - Jin-Guo Liu
AU - Xin Wang
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11792
UR - https://arxiv.org/abs/2609.11792
AB - 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.
ER -