Neural network wave functions and the sign problem
This addresses a major bottleneck in applying neural networks to quantum many-body physics, with implications for variational Monte Carlo methods, though it is incremental in proposing a specific architectural improvement.
The paper tackled the challenge of neural quantum states struggling to converge to ground states with nontrivial sign structures in lattice models by proposing a neural network architecture with an explicit phase ansatz, achieving state-of-the-art variational energies for antiferromagnets and uncovering low-energy states inconsistent with expected ground states.
Neural quantum states (NQS) are a promising approach to study many-body quantum physics. However, they face a major challenge when applied to lattice models: Convolutional networks struggle to converge to ground states with a nontrivial sign structure. We tackle this problem by proposing 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 latter case, our approach uncovers low-energy states that exhibit the Marshall sign rule and are therefore inconsistent with the expected ground state. Such states are the likely cause of the obstruction for NQS-based variational Monte Carlo to access the true ground states of these systems. We discuss the implications of this observation and suggest potential strategies to overcome the problem.