论文标题
二维绝缘子中的定位各向异性和复杂的几何形状
Localization anisotropy and complex geometry in two-dimensional insulators
论文作者
论文摘要
定位张量是绝缘子和金属之间区分性的量度。该张量与动量空间中与被占用条带相关的量子度量张量有关。在二维和热力学极限中，它在扭曲的空间上定义了一个平坦的riemannian度量，从拓扑上讲是一个圆环，该空间赋予了该空间的复杂结构，由复杂的参数$τ$描述。结果表明，后者是与系统各向异性有关的物理观察。数量$τ$和扭曲角度的riemannian体积提供了一种不变的方法，可以参数在热力学极限中获得的平坦量子公制。此外，如果通过更改理论的耦合，系统会经历差距截断的量子相变，尽管度量分解（金属状态），则复杂的结构$τ$仍然是很好的定义，并且它是由hamiltonian在差距闭合点附近的汉密尔顿的形式固定的。 Riemannian体积负责该相转换时度量的差异。
The localization tensor is a measure of distinguishability between insulators and metals. This tensor is related to the quantum metric tensor associated with the occupied bands in momentum space. In two dimensions and in the thermodynamic limit, it defines a flat Riemannian metric over the twist-angle space, topologically a torus, which endows this space with a complex structure, described by a complex parameter $τ$. It is shown that the latter is a physical observable related to the anisotropy of the system. The quantity $τ$ and the Riemannian volume of the twist-angle space provide an invariant way to parametrize the flat quantum metric obtained in the thermodynamic limit. Moreover, if by changing the couplings of the theory, the system undergoes quantum phase transitions in which the gap closes, the complex structure $τ$ is still well defined, although the metric diverges (metallic state), and it is fixed by the form of the Hamiltonian near the gap closing points. The Riemannian volume is responsible for the divergence of the metric at the phase transition.
