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Topological invariants for interacting topological insulators. Ⅱ. Breakdown of single-particle Green's function formalism

机译：用于交互拓扑绝缘子的拓扑不变量。 Ⅱ。单粒子格林函数形式主义的分解

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Topological phase transitions in free fermion systems can be characterized by the closing of single-particle gap and the change in topological invariants. However, in the presence of electronic interactions, topological phase transitions can be more complicated. In paper Ⅰ of this series [Phys. Rev. B 93, 195163 (2016)], we have proposed an efficient scheme to evaluate the topological invariants based on the single-particle Green's function formalism. Here, in paper Ⅱ, we demonstrate several interaction-driven topological phase transitions (TPTs) in two-dimensional (2D) interacting topological insulators (TIs) via large-scale quantum Monte Carlo (QMC) simulations, based on the scheme of evaluating topological invariants presented in paper Ⅰ. Across these transitions, the defining symmetries of the TIs have been neither explicitly nor spontaneously broken. In the first two models, the topological invariants calculated from the Green's function formalism succeed in characterizing the topologically distinct phases and identifying interaction-driven TPTs. However, in the other two models, we find that the single-particle gap does not close and the topological invariants constructed from the single-particle Green's function acquire no change across the TPTs. Unexpected breakdown of the Green's function formalism in constructing the topological invariants is thus discovered. We thence classify the topological phase transitions in interacting TIs into two categories in practical computation: Those that have noninteracting correspondence can be characterized successfully by the topological invariants constructed from the Green's functions, while for the others that do not have noninteracting correspondence, the Green's function formalism experiences a breakdown, but more interesting and exciting phenomena, such as emergent collective critical modes at the transition, arise. Discussion on the success and breakdown of topological invariants constructed from the Green's function formalism in the context of symmetry protected topological (SPT) states is presented.
机译：自由费米子系统中的拓扑相变可以通过单粒子间隙的闭合和拓扑不变性的变化来表征。但是，在存在电子相互作用的情况下，拓扑相变可能会更加复杂。在该系列的论文Ⅰ中。 B 93，195163（2016）Rev.]，我们提出了一种有效的方案，用于基于单粒子Green函数形式主义来评估拓扑不变量。在本文Ⅱ中，我们基于大规模的拓扑评估方案，通过大规模量子蒙特卡罗（QMC）模拟，展示了二维（2D）相互作用的拓扑绝缘体（TI）中的几个相互作用驱动的拓扑相变（TPT）不变性在论文Ⅰ中提出。在这些过渡过程中，TI的定义对称既没有明确也没有自发打破。在前两个模型中，根据格林函数形式主义计算出的拓扑不变量成功地表征了拓扑上不同的阶段，并确定了交互驱动的TPT。但是，在其他两个模型中，我们发现单粒子间隙没有关闭，并且由单粒子格林函数构造的拓扑不变量在TPT之间没有任何变化。因此发现了在构造拓扑不变量时格林函数形式主义的意外崩溃。因此，在实际计算中，我们将交互TI的拓扑相变分为两类：具有非交互对应关系的拓扑相变可以通过Green函数构造的拓扑不变量来成功表征，而对于其他不具有非交互对应关系的拓扑不变量，则采用Green函数。形式主义经历了崩溃，但是出现了更有趣和令人兴奋的现象，例如在过渡时期出现的集体批判模式。讨论了在对称受保护拓扑（SPT）状态的背景下，由格林函数形式主义构造的拓扑不变量的成功与否。

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    《Physical review》 |2016年第19期|195164.1-195164.13|共13页
  • 作者

    Yuan-Yao He; Han-Qing Wu; Zi Yang Meng; Zhong-Yi Lu;

  • 作者单位

    Department of Physics, Renmin University of China, Beijing 100872, China;

    Department of Physics, Renmin University of China, Beijing 100872, China;

    Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;

    Department of Physics, Renmin University of China, Beijing 100872, China;

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