Simulating Strongly Interacting Two-dimensional Quantum Materials with Neural Network

Two-dimensional quantum materials offer a unique platform for investigating quantum phases of matter, yet solving many-electron problems in these systems is challenging due to strong correlation effects. We develop new kinds of neural wavefunction—a variational representation of quantum states designed to efficiently address these challenges. We develop a neural network that augments a BCS-type geminal wavefunction with a message-passing graph neural network-parameterized pair amplitude, enabling accurate and scalable simulations of many-electron systems. Using variational Monte Carlo, we apply this approach to two-dimensional electron-hole bilayers, accurately capturing interaction-induced phases, including exciton Bose-Einstein condensates, electron-hole superconductors, and bilayer Wigner crystals. Furthermore, we introduce and develop neural Bloch wavefunction to the semiconductor heterobilayer WSe₂/WS₂. Our method captures phases such as the generalized Wigner crystal at filling factor n=1/3, a Mott insulator at n=1, and a correlated insulator with local magnetic moments and antiferromagnetic spin correlation at n=2. Together, these neural network-based methods demonstrate the potential of physically-motivated wavefunctions to enhance quantum material simulations and uncover new phases within a unified framework.