标题： $\mathbb{Z}_2$ FTR 对称微分算子的分类与Anderson 局域化的障碍 显示英文标题

标题： $\mathbb{Z}_2$ classification of FTR symmetric differential operators and obstruction to Anderson localization

摘要： 本文涉及在欧几里得平面上费米时间反演（FTR）对称部分微分哈密顿量的$\mathbb{Z}_2$分类。 我们考虑两种绝缘体被界面隔开的情况。 在沿界面的空间平移下不变的哈密顿量根据是否可以通过连续变形带隙分为两类。 引入一个相关的奇对称弗雷德霍姆算子，我们证明该分类在FTR对称扰动下是稳定的。 非平凡哈密顿量不能带隙的性质可以解释为安德森局域化的拓扑障碍：无论系统中存在多少（空间紧支撑的）扰动，在非平凡相中都保证在两个方向上存在一定量的传输。 我们为这类系统提出了散射理论，并通过数值计算表明，在存在FTR对称扰动的情况下传输确实得到保证，而对于非对称波动则不再如此。 显示英文摘要

摘要： This paper concerns the $\mathbb{Z}_2$ classification of Fermionic Time-Reversal (FTR) symmetric partial differential Hamiltonians on the Euclidean plane. We consider the setting of two insulators separated by an interface. Hamiltonians that are invariant with respect to spatial translations along the interface are classified into two categories depending on whether they may or may not be gapped by continuous deformations. Introducing a related odd-symmetric Fredholm operator, we show that the classification is stable against FTR-symmetric perturbations. The property that non-trivial Hamiltonians cannot be gapped may be interpreted as a topological obstruction to Anderson localization: no matter how much (spatially compactly supported) perturbations are present in the system, a certain amount of transmission in both directions is guaranteed in the nontrivial phase. We present a scattering theory for such systems and show numerically that transmission is indeed guaranteed in the presence of FTR-symmetric perturbations while it no longer is for non-symmetric fluctuations.