标题： 一维系统的拓扑结点 显示英文标题

标题： Topological junctions for one-dimensional systems

摘要： 我们研究并分类了一维材料连接处保护边缘模式的出现。 利用边界辛空间中拉格朗日平面的对称性，我们提出了对一维拓扑绝缘体周期表的新证明。 我们表明，具有不同拓扑指标的两种材料的连接处必然会出现边缘模式。 我们的方法为理解一维中的对称性保护模式提供了一个系统框架。 它不依赖于周期性或遍历性，并涵盖了包括连续和离散模型在内的广泛算子。 显示英文摘要

摘要： We study and classify the emergence of protected edge modes at the junction of one-dimensional materials. Using symmetries of Lagrangian planes in boundary symplectic spaces, we present a novel proof of the periodic table of topological insulators in one dimension. We show that edge modes necessarily arise at the junction of two materials having different topological indices. Our approach provides a systematic framework for understanding symmetry-protected modes in one-dimension. It does not rely on periodic nor ergodicity and covers a wide range of operators which includes both continuous and discrete models.