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Identification of emergent constraints and hidden order in frustrated magnets using tensorial kernel methods of machine learning

机译：使用张于机器学习方法识别令人沮丧的磁铁中的紧急约束和隐藏顺序

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摘要

Machine-learning techniques have proved successful in identifying ordered phases of matter. However, it remains an open question how far they can contribute to the understanding of phases without broken symmetry, such as spin liquids. Here we demonstrate how a machine-learning approach can automatically learn the intricate phase diagram of a classical frustrated spin model. The method we employ is a support vector machine equipped with a tensorial kernel and a spectral graph analysis which admits its applicability in an effectively unsupervised context. Thanks to the interpretability of the machine we are able to infer, in closed form, both order parameter tensors of phases with broken symmetry, and the local constraints which signal an emergent gauge structure, and so characterize classical spin liquids. The method is applied to the classical XXZ model on the pyrochlore lattice where it distinguishes, among others, between a hidden biaxial spin-nematic phase and several different classical spin liquids. The results are in full agreement with a previous analysis by Taillefumier et al. [Phys. Rev. X 7, 041057 (2017)], but go further by providing a systematic hierarchy between disordered regimes, and establishing the physical relevance of the susceptibilities associated with the local constraints. Our work paves the way for the search of new orders and spin liquids in generic frustrated magnets.
机译：在识别物质阶段的情况下，已经成功地证明了机器学习技术。然而，它仍然是他们有多远的问题，他们可以有助于了解没有破裂对称的相位，例如旋转液体。在这里，我们展示了机器学习方法如何自动学习经典沮丧的旋转模型的复杂相图。我们采用的方法是配备有张力核的支持向量机和一个光谱图分析，可在有效无监督的背景下承认其适用性。由于该机器的可解释性，我们能够以封闭形式推断，两顺序参数张相张差，具有破损的对称性，以及信号的局部约束，信号表征古典旋转液体。该方法应用于Pyrochlore格的经典XXZ模型，其中在隐藏的双轴旋转向列和几种不同的典型旋转液体之间区分。结果与Taillefumier等人的先前分析完全一致。 [物理。 Rev. x 7,041057（2017）]，但通过在无序制度之间提供系统等级，并进一步进一步进一步，并建立与局部限制相关的敏感性的物理相关性。我们的工作为在通用沮丧的磁铁中搜索新订单和旋转液体的方式铺平了道路。

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  • 来源
    《Physical review》 |2019年第17期|174408.1-174408.20|共20页
  • 作者

    Greitemann Jonas; Liu Ke; Jaubert Ludovic D. C.; Yan Han; Shannon Nic; Pollet Lode;

  • 作者单位

    Univ Munich Arnold Sommerfeld Ctr Theoret Phys Theresienstr 37 D-80333 Munich Germany|MCQST Schellingstr 4 D-80799 Munich Germany;

    Univ Munich Arnold Sommerfeld Ctr Theoret Phys Theresienstr 37 D-80333 Munich Germany|MCQST Schellingstr 4 D-80799 Munich Germany;

    Univ Bordeaux CNRS LOMA UMR 5798 F-33400 Talence France;

    Okinawa Inst Sci & Technol Grad Univ Theory Quantum Matter Unit Onna Okinawa 9040412 Japan;

    Okinawa Inst Sci & Technol Grad Univ Theory Quantum Matter Unit Onna Okinawa 9040412 Japan;

    Univ Munich Arnold Sommerfeld Ctr Theoret Phys Theresienstr 37 D-80333 Munich Germany|MCQST Schellingstr 4 D-80799 Munich Germany|Shanghai Jiao Tong Univ Wilczek Quantum Ctr Sch Phys & Astron Shanghai 200240 Peoples R China;

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