We develop a pairing-based graph neural network for simulating quantum many-body systems. Our architecture augments a BCS-type geminal wavefunction with a generalized pair amplitude parameterized by a graph neural network. Variational Monte Carlo with our neural network simultaneously provides an accurate, flexible, and scalable method for simulating many-electron systems. We apply this method to two-dimensional semiconductor electron-hole bilayers and obtain 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.

翻译：我们开发了一种基于配对的图神经网络，用于模拟量子多体系统。该架构通过图神经网络参数化的广义配对振幅，增强了BCS类型的geminal波函数。结合该神经网络的变分蒙特卡洛方法，为模拟多电子系统提供了一种准确、灵活且可扩展的方案。我们将该方法应用于二维半导体电子-空穴双层系统，并在多种相互作用诱导的相态中获得了精确结果，包括激子玻色-爱因斯坦凝聚、电子-空穴超导体以及双层维格纳晶体。本研究证明了物理启发的神经网络波函数在量子材料模拟中的潜力。