Neural network wave functions and the sign problem

TL;DR

This paper introduces a neural network architecture with an explicit phase ansatz to better represent complex sign structures in quantum many-body systems, improving variational energy estimates and highlighting challenges in accessing true ground states.

Contribution

The authors propose a novel neural network architecture with an interpretable phase ansatz that enhances the ability of neural quantum states to handle sign problems in lattice models.

Findings

Achieves state-of-the-art variational energies for antiferromagnets.

Uncovers low-energy states following the Marshall sign rule.

Identifies sign structure as a key obstacle in neural quantum state methods.

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.