We introduce a pairing-based graph neural network, $\textit{GemiNet}$, for simulating quantum many-body systems. Our architecture augments a BCS mean-field wavefunction with a generalized pair amplitude parameterized by a graph neural network. Variational Monte Carlo with GemiNet simultaneously provides an accurate, flexible, and scalable method for simulating many-electron systems. We apply GemiNet to two-dimensional semiconductor electron-hole bilayers and obtain highly accurate results on a variety of interaction-induced phases, including the exciton Bose-Einstein condensate, electron-hole superconductor, and bilayer Wigner crystal. Our study demonstrates the potential of physically-motivated neural network wavefunctions for quantum materials simulations.

使用基于配对的图神经网络$	extit{GemiNet}$模拟量子多体系统，通过将BCS均场波函数与由图神经网络参数化的广义配对振幅相结合，我们的架构提供了一种准确、灵活、可扩展的方法来模拟多电子系统。将GemiNet应用于二维半导体电子-空穴双层，并获得了在各种相互作用引起的相变中的高精度结果，包括激子玻色-爱因斯坦凝聚、电子-空穴超导体和双层维格纳晶体。我们的研究展示了以物理为基础的神经网络波函数在量子材料模拟中的潜力。

基于配对的图神经网络用于模拟量子材料