论文标题
Majorana纳米线，Kitaev链和自旋模型
Majorana nanowires, Kitaev chains, and spin models
论文作者
论文摘要
由理想化的Kitaev链玩具模型和实验性半导体 - 驱动器Majorawara纳米线既可以托管Majoraana零模式，我们从理论上研究两个模型在多大程度上是等效的或类似的，使用两者的相应的双旋转模型在多大程度上研究了这个问题。我们从基塔夫链与横向场XY自旋模型之间的双重性开始，以建立基塔夫链与纳米线之间的连接。通过将Jordan-Wigner转换应用于纳米线，我们发现相应的骨体旋转模型是一种广义的自旋群集模型，其中包含带有交错耦合的3旋和4-旋转项。通过用更高的能量投射出裸半导体的上部频带，我们从拓扑状态深处的稀疏纳米线系统中获得了有效的低能无旋转系统。最后，我们通过证明无旋转的基塔夫链可以看作是拓扑状态深处的一阶近似值，从而建立了Kitaev链和Majoraana纳米线之间的联系。
Motivated by the fact that the idealized Kitaev chain toy model and the experimental semiconductor-superconductor Majorana nanowire can both host the Majorana zero modes, we theoretically investigate the question to what extent the two models are equivalent or similar, using the perspective of the corresponding dual spin models for both. We start with the duality between the Kitaev chain and the transverse-field XY spin model through the Jordan-Wigner transformation with the goal of establishing the connection between the Kitaev chain and the nanowire. By applying the Jordan-Wigner transformation to the nanowire, we find that the corresponding bosonic spin model is a generalized spin cluster model, containing 3-spin and 4-spin terms, with staggered couplings. By projecting out the upper band of the bare semiconductor with higher energy, we obtain an effective low-energy spinless system from the spinful nanowire system deep in the topological regime. Finally, we establish the connection between the Kitaev chain and Majorana nanowire by showing that the spinless Kitaev chain can be viewed as the first-order approximation of the spinful Majorana nanowire deep in the topological regime.
