Neural network wave functions and the sign problem

• Published in: Physical review research Vol. 2; no. 3; p. 033075
• Main Authors: Szabó, Attila, Castelnovo, Claudio
• Format: Journal Article
• Language: English
• Published: American Physical Society 15.07.2020
• ISSN: 2643-1564; 2643-1564
• DOI: 10.1103/PhysRevResearch.2.033075

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.