We derive the topological Kondo Hamiltonian describing a Y junction of three XX-spin chains connected to outer quantum Ising chains with different tilting angles for the Ising axis. We show that the tilting angles in the spin models play the role of the phases of the superconducting order parameters at the interfaces between bulk superconductors and one-dimensional conducting normal electronic wires. As a result, different tilting angles induce nonzero equilibrium spin (super)currents through the junction. Employing the renormalization group approach to the topological Kondo model, we derive the scaling formulas for the equilibrium spin currents. We argue that, by monitoring the crossover in the currents induced by the Kondo effect, it is possible to estimate the Kondo screening length. In particular, we prove how it is possible to tune the Kondo length by acting on the applied phases only; this enables us to map out the scaling properties by just tuning the tilting angles and the Kondo length accordingly.

我们得出拓扑近藤哈密顿量，它描述了三个XX自旋链的Y结，这些XX自旋链连接到外部Ising轴的不同Ising轴倾斜角。我们显示自旋模型中的倾斜角在块状超导体和一维导电法线之间的界面上起着超导有序参数相位的作用。结果，不同的倾斜角会引起通过结的非零平衡自旋（超）电流。通过对拓扑Kondo模型使用归一化组方法，我们得出了平衡自旋电流的缩放公式。我们认为，通过监视近藤效应引起的电流交叉，可以估计近藤屏蔽的长度。尤其是，我们证明了仅通过作用于所应用的相位就可以调整近藤长度。这使我们能够通过仅调整倾斜角度和近藤长度来绘制缩放属性。