Permutation invariant multi-scale full quantum neural network wavefunction
Abstract
Solving the intricate quantum behavior of interacting particles is key to unlocking the mysteries of condensed matter, but capturing their complex correlations across different scales remains a monumental challenge. We introduce a neural network framework that overcomes this barrier by modeling the full quantum wavefunction of a system, including electrons, nuclei and muons, directly capturing the full quantum effects beyond the Born-Oppenheimer approximation. The neural network approximates joint wavefunction of different interacting particles with a rigorous handling of permutation invariance, enabling simultaneous treatment of nuclear quantum effects and electron-nucleus-muon couplings without explicit excited states. Validated on molecular systems, this approach offers a computationally feasible way to model full quantum phenomena in complex many-body systems, establishing a direct connection between fundamental particle properties and emergent material behavior.
Keywords
Cite
@article{arxiv.2603.12233,
title = {Permutation invariant multi-scale full quantum neural network wavefunction},
author = {Pengzhen Cai and Yubing Qian and Li Deng and Weizhong Fu and Lei Yang and Zhiyu Sun and Xin-Zheng Li and En-Ge Wang and Liangwen Chen and Weiluo Ren and Ji Chen},
journal= {arXiv preprint arXiv:2603.12233},
year = {2026}
}