(455b) Neural Network Wave Function Solver

By simulating atoms and electrons following the laws of quantum mechanics, we can obtain virtually all material properties of interest. Since the many-body wave function naively scales exponentially with number of particles, we use approximate methods to solve the time-independent Schrödinger equation. Variational quantum Monte Carlo is a polynomial scaling method that reaches high accuracy which depends on the form of the trial wave function. Neural networks have been used to parameterize the orbitals of the Slater determinant, and these ansatzes reached state-of-the-art accuracies on molecules. However, optimization and scaling become difficult as system size increases, and previous work has fixed all electrons' spins throughout training and focused on molecules over solids. We built the first neural network wave function for solids that has correct invariances to supercell translation and point symmetries of the space group. We show that symmetrizing over space group operations reaches ground-state energies with higher scalability than other ansatzes. We also allow for variable electron spin on the Bloch sphere, and include spin information in the neural network input, dot-product with orbitals, and spin sampling in the MCMC chain. Our continuous spin wave functions achieve better energies than previous NN wave functions on molecules, the periodic hydrogen chain, and periodic homogeneous electron gas. We show that spin sampling leads to largest improvements in physical systems that are expected to have frustrated spin. Our work opens the possibility of direct investigation of complex quantum phenomena in solids and spin systems.