We use determinant quantum Monte Carlo (DQMC), in combination with the principal component analysis (PCA) approach to unsupervised learning, to extract information about phase transitions in several of the most fundamental Hamiltonians describing strongly correlated materials. We first explore the zero-temperature antiferromagnet to singlet transition in the periodic Anderson model, the Mott insulating transition in the Hubbard model on a honeycomb lattice, and the magnetic transition in the 1/6-filled Lieb lattice. We then discuss the prospects for learning finite temperature superconducting transitions in the attractive Hubbard model, for which there is no sign problem. Finally, we investigate finite temperature charge density wave (CDW) transitions in the Holstein model, where the electrons are coupled to phonon degrees of freedom, and carry out a finite size scaling analysis to determine $T_c$. We examine the different behaviors associated with Hubbard-Stratonovich auxiliary field configurations on both the entire space-time lattice and on a single imaginary time slice, or other quantities, such as equal-time Green's and pair-pair correlation functions.

中文翻译：

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费米离子临界点的主成分分析

我们将行列式量子蒙特卡洛（DQMC）与主成分分析（PCA）方法结合使用以进行无监督学习，以提取描述最相关材料的一些最基本的哈密顿量中有关相变的信息。我们首先在周期性的安德森模型中探索从零温度反铁磁体到单重态的跃迁，在蜂窝晶格上的哈伯德模型中的Mott绝缘跃迁，以及在1/6填充的李布晶格中的磁跃迁。然后，我们讨论了在有吸引力的Hubbard模型中学习有限温度超导跃迁的前景，该模型没有符号问题。最后，我们研究了Holstein模型中的有限温度电荷密度波（CDW）跃迁，其中电子与声子自由度耦合，${Ť}_C$。我们研究了在整个时空晶格和单个虚时切片或其他数量（例如等时格林和成对对相关函数）上与Hubbard-Stratonovich辅助场配置相关的不同行为。