论文标题
基塔夫链中几何挫败感的影响
Effects of geometric frustration in Kitaev chains
论文作者
论文摘要
我们研究了基塔夫链的拓扑相变，这是由于增加了单个长期跳跃而引起的几何挫败感。后一种情况定义了缺乏翻译不变性的腿环几何形状（Kitaev Tie）。为了研究系统的拓扑特性，我们概括了研究Majorana模式的出现的转移矩阵方法。我们发现几何挫败感引起了拓扑相图，在这种拓扑相图中，非平凡阶段与琐碎的阶段在变化的额外跳跃范围和化学势范围内交替出现。在由多个小区域组成的翻译模型中还研究了挫败感效果。在后一个系统中，转化不变性允许使用拓扑散装不变式来确定相图和散装对应关系。已经证明，即使恢复了翻译不变性，几何挫败感效果仍然存在。这些发现与研究循环弹道导体的拓扑阶段有关。
We study the topological phase transitions of a Kitaev chain in the presence of geometric frustration caused by the addition of a single long-range hopping. The latter condition defines a legged-ring geometry (Kitaev tie) lacking of translational invariance. In order to study the topological properties of the system, we generalize the transfer matrix approach through which the emergence of Majorana modes is studied. We find that geometric frustration gives rise to a topological phase diagram in which non-trivial phases alternate with trivial ones at varying the range of the extra hopping and the chemical potential. Frustration effects are also studied in a translational invariant model consisting of multiple-ties. In the latter system, the translational invariance permits to use the topological bulk invariant to determine the phase diagram and bulk-edge correspondence is recovered. It has been demonstrated that geometric frustration effects persist even when translational invariance is restored. These findings are relevant in studying the topological phases of looped ballistic conductors.
