Neural network wave functions and the sign problem

Neural quantum states are a promising approach to study many-body quantum physics. However, they face a major challenge when applied to lattice models: Neural networks struggle to converge to ground states with a nontrivial sign structure. In this talk, I present a neural network architecture with a simple, explicit, and interpretable phase ansatz, which can robustly represent such states and achieve state-of-the-art variational energies for both conventional and frustrated antiferromagnets. In the first case, the neural network correctly recovers the Marshall sign rule without any prior knowledge. For frustrated magnets, our approach uncovers low-energy states that exhibit the Marshall sign rule but does not reach the true ground state, which is expected to have a different sign structure. I discuss strategies for overcoming this "residual sign problem" that may allow using neural quantum states for challenging spin liquid problems.