Quantum gas systems are ideal analog quantum simulation platforms for tackling some of the most challenging problems in strongly correlated quantum matter. However, they also expose the urgent need for new theoretical frameworks. Simple models in one dimension, well studied with conventional methods, have received considerable recent attention as test cases for new approaches. Ladder models provide the logical next step, where established numerical methods are still reliable, but complications of higher dimensional effects like gauge fields can be introduced. In this paper, we investigate the application of the recently developed neural-network quantum states in the two-leg Bose-Hubbard ladder under strong synthetic magnetic fields. Based on the restricted Boltzmann machine and feedforward neural network, we show that variational neural networks can reliably predict the superfluid-Mott insulator phase diagram in the strong coupling limit comparable with the accuracy of the density-matrix renormalization group. In the weak coupling limit, neural networks also diagnose other many-body phenomena like the vortex, chiral and biased-ladder phases. Our work demonstrates that the two-leg Bose-Hubbard model with magnetic flux is an ideal test ground for future developments of neural-network quantum states.

中文翻译：

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磁通量下两腿 Bose-Hubbard 阶梯的神经网络量子态

量子气体系统是理想的模拟量子模拟平台，用于解决强相关量子物质中一些最具挑战性的问题。然而，它们也暴露了对新理论框架的迫切需求。一维的简单模型，用传统方法进行了很好的研究，最近作为新方法的测试用例受到了相当大的关注。阶梯模型提供了合乎逻辑的下一步，其中已建立的数值方法仍然可靠，但可能会引入诸如规范场之类的高维效应的复杂性。在本文中，我们研究了最近开发的神经网络量子态在强合成磁场下的两条腿 Bose-Hubbard 梯子中的应用。基于受限玻尔兹曼机和前馈神经网络，我们表明，变分神经网络可以可靠地预测强耦合极限下的超流体-莫特绝缘体相图，与密度矩阵重整化组的精度相当。在弱耦合极限下，神经网络还可以诊断其他多体现象，例如涡旋、手征和偏梯相。我们的工作表明，具有磁通量的两腿 Bose-Hubbard 模型是神经网络量子态未来发展的理想试验场。