Optimizing Neural Network Backflow for Ab-initio Solid Calculations

Neural quantum states (NQS) are rapidly emerging as a powerful ansatz for computational quantum many-body physics. While NQS methods have seen significant success in ab-initio quantum chemistry, their application to ab-initio solids remains relatively unexplored. We aim to bridge this gap by developing a neural network backflow (NNBF) wave function tailored for periodic systems. Our approach extends and improves upon algorithms previously developed for quantum chemistry, incorporating efficient sampling schemes, streamlined local energy computations, more effective optimization methods, and enhancements to the ansatz's expressivity. We benchmark these developments on large-scale 1D hydrogen chains and other periodic materials. Our results demonstrate that this enhanced NNBF framework allows for highly efficient and accurate ab-initio simulations of periodic solids.