论文标题
相关电子系统中布里鲁因区域的量子公制及其与Chern绝缘子拓扑的关系
Quantum metric on the Brillouin Zone in correlated electron systems and its relation to topology for Chern insulators
论文作者
论文摘要
物理学的几何方面在现代冷凝物理物理学中起着至关重要的作用。量子度量是这些几何量之一，它定义了参数空间上的距离，并有助于各种物理现象，例如超导性和非线性电导率。尽管它很重要，但相互作用系统中的量子指标知之甚少。在本文中，我们在布里远的相关电子系统上引入了广义量子公制（GQM）。该量子度量基于单粒子绿色功能编写的光导率。我们从分析上证明，该定义等于非互动系统中量子指标的现有定义，并且对于度量标准而言，它是正式的半明确定义。此外，我们指出了相互作用系统中GQM与Chern号之间的关系。然后，我们在数值上确认具有和不相互作用的Qi-wu-zhang模型中GQM的这些属性。我们认为，GQM将是将量子指标推广到相互作用制度的一步。
Geometric aspects of physics play a crucial role in modern condensed matter physics. The quantum metric is one of these geometric quantities which defines the distance on a parameter space and contributes to various physical phenomena, such as superconductivity and nonlinear conductivity. Despite its importance, the quantum metric in interacting systems is poorly understood. In this paper, we introduce a generalized quantum metric(GQM) on the Brillouin zone for correlated electron systems. This quantum metric is based on the optical conductivity that is written by single-particle Green's functions. We analytically prove that this definition is equivalent to the existing definition of the quantum metric in noninteracting systems and that it is positive semi-definite as necessary for a metric. Furthermore, we point out the relationship between the GQM and the Chern number in interacting systems. We then numerically confirm these properties of the GQM in the Qi-Wu-Zhang model with and without interaction. We believe that the GQM will be a step toward generalizing the quantum metric to the interacting regime.
