Neural network wave functions and the sign problem

• URL: http://arxiv.org/abs/2002.04613v3
• Date: Thu, 30 Jul 2020 16:17:21 GMT
• Title: Neural network wave functions and the sign problem
• Abstract summary: We propose a neural network architecture with a simple, explicit, and interpretable phase ansatz. We find that low-energy states that exhibit the Marshall sign rule are 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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