空间调制下Majorana链的拓扑量子相变
Topological quantum phase transitions in a Majorana chain with spatial modulation
摘要：
数值研究了一维广义Kitaev模型中化学势周期性调制时的量子相变和Majorana零模的稳定性。利用开边界条件下的精确对角化方法，我们从纠缠谱和弦关联函数等非局域性质出发，研究了基态相位。当我们改变调制的相位时，Majorana零模的数量发生变化，这表现在ES的最低能级的简并性上。接下来，我们研究了由调制幅度的变化驱动的量子相变。特别是，对于某些值的波数和相位的调制，我们观察到一个量子相变从一个拓扑相位到另一个弦的关联函数在空间振荡。我们还展示了一种情况下，退化的ES不改变，即使足够大的幅度的调制。最后，利用反映零能激励个数的拓扑不变量来刻画周期边界条件下系统的相位。
英文摘要：
We numerically study the quantum phase transitions and the stability of Majorana zero modes in a generalized Kitaev model in one dimension when the chemical potential is periodically modulating in space. By using the exact diagonalization method for open boundary condition, we investigate the ground-state phases in terms of the non-local properties such as the entanglement spectrum (ES) and the string correlation functions. When we vary the phase of the modulation, the number of the Majorana zero modes changes, which manifests itself in the degeneracy of the lowest level of the ES. Next, we study the quantum phase transitions driven by the change in the amplitude of the modulation. In particular, for certain values of the wave number and the phase of the modulation, we observe a quantum phase transition from one topological phase into another where the string correlation function oscillates in space. We also show a case where the degeneracy of the ES does not change even for large enough amplitude of the modulation. Finally, we characterize the phases of the system with periodic boundary condition by the topological invariant, which reflects the number of the zero-energy excitations.
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