Machine learning offers an unprecedented perspective for the problem of
classifying phases in condensed matter physics. We employ neural-network
machine learning techniques to distinguish finite-temperature phases of the
strongly correlated fermions on cubic lattices. We show that a three
dimensional convolutional network trained on auxiliary field configurations
produced by quantum Monte Carlo simulations of the Hubbard model can correctly
predict the magnetic phase diagram of the model at the average density of one
(half filling). We then use the network, trained at half filling, to explore
the trend in the transition temperature as the system is doped away from half
filling. This transfer learning approach predicts that the instability to the
magnetic phase extends to at least 5% doping in this region. Our results pave
the way for other machine learning applications in correlated quantum many-body
systems.

使用神经网络机器学习技术，在辅助场配置上训练三维卷积网络，成功预测了半填充下哈伯模型的磁相图，并利用迁移学习方法预测了磁相的不稳定性扩展到了至少 5% 的掺杂度，显示了在相关量子多体系统中运用机器学习的广阔前景。