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Z_2 gauge theory for valence bond solids on the kagome lattice

机译：Kagome晶格上价键固体的Z_2规理论

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摘要

We present an effective Z_2 gauge theory that captures various competing phases in spin-1/2 kagome lattice antiferromagnets: the topological Z_2 spin liquid (SL) phase, and the 12-site and 36-site valence bond solid (VBS) phases. Our effective theory is a generalization of the recent Z_2 gauge theory proposed for SL phases by Wan and Tchernyshyov. In particular, we investigate possible VBS phases that arise from vison condensations in the SL. In addition to the 12-site and 36-site VBS phases, there exists 6-site VBS that is closely related to the symmetry-breaking valence bond modulation patterns observed in the recent density matrix renormalization group simulations. We find that our results have remarkable consistency with a previous study using a different Z_2 gauge theory. Motivated by the lattice geometry in the recently reported vanadium oxyfluoride kagome antiferromagnet, our gauge theory is extended to incorporate lowered symmetry by inequivalent up and down triangles. We investigate effects of this anisotropy on the 12-site, 36-site, and 6-site VBS phases. The 12-site VBS is stable to anisotropy while the 36-site VBS undergoes severe dimer melting. Interestingly, any analog of the 6-site VBS is not found in this approach. We discuss the implications of these findings and also compare the results with a different type of Z_2 gauge theory used in previous studies.
机译：我们提出了一个有效的Z_2量规理论，该理论捕获了自旋1/2 kagome晶格反铁磁体中的各种竞争相：拓扑Z_2自旋液体（SL）相以及12位和36位价键固相（VBS）相。我们的有效理论是对Wan和Tchernyshyov针对SL相提出的最新Z_2规范理论的概括。特别是，我们研究了SL中的光子凝结可能引起的VBS相。除了12位和36位VBS相之外，还存在6位VBS，这与在最近的密度矩阵重整化组模拟中观察到的对称断裂价键调制模式密切相关。我们发现我们的结果与以前使用不同Z_2规范理论的研究具有显着一致性。受最近报道的氟氧化钒kagome反铁磁体中晶格几何形状的影响，我们的量规理论已扩展为通过不等价的上下三角形合并降低的对称性。我们调查这种各向异性对12位，36位和6位VBS相的影响。 12位VBS对各向异性稳定，而36位VBS经历严重的二聚体熔化。有趣的是，这种方法没有找到6位VBS的任何类似物。我们讨论了这些发现的含义，还将结果与先前研究中使用的不同类型的Z_2规范理论进行了比较。

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  • 来源
    《Physical review》 |2015年第20期|205131.1-205131.16|共16页
  • 作者

    Kyusung Hwang; Yejin Huh; Yong Baek Kim;

  • 作者单位

    Department of Physics and Centre for Quantum Materials, University of Toronto, Toronto, Ontario, Canada M5S 1A7;

    Department of Physics and Centre for Quantum Materials, University of Toronto, Toronto, Ontario, Canada M5S 1A7;

    Department of Physics and Centre for Quantum Materials, University of Toronto, Toronto, Ontario, Canada M5S 1A7,Canadian Institute for Advanced Research/Quantum Materials Program, Toronto, Ontario, Canada MSG 1Z8,School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea;

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  • 原文格式 PDF
  • 正文语种 eng
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  • 关键词

    quantized spin models; antiferromagnetics;

    机译：量化自旋模型反铁磁;

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