We study analytically topological properties of a noninteracting modified dimerized Kitaev chain and an exactly solvable interacting dimerized Kitaev chain under open boundary conditions by analyzing two introduced edge correlation functions. The interacting dimerized Kitaev chain at the symmetry point $\mathrm{\Delta }=t$ and the chemical potential $\mu =0$ can be exactly solved by applying two Jordan-Wigner transformations and a spin rotation, which permits us to calculate the edge correlation functions analytically. We demonstrate that the two edge correlation functions can be used to characterize the trivial, Su-Schrieffer-Heeger-like topological and topological superconductor phases of both the noninteracting and interacting systems and give their phase diagrams.

中文翻译：

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通过边缘相关函数表征二聚化Kitaev链的拓扑相

我们通过分析两个引入的边缘相关函数，研究了在开放边界条件下非相互作用的修饰二聚化Kitaev链和可精确相互作用的二聚化Kitaev链的分析拓扑性质。对称点处相互作用的二聚化Kitaev链$\mathrm{\Delta }=Ť$ 和化学势 $\mu =0$可以通过应用两个Jordan-Wigner变换和一个自旋旋转来精确解决，这使我们能够分析性地计算边缘相关函数。我们证明了两个边缘相关函数可用于表征非相互作用和相互作用系统的琐碎的，类似于Su-Schrieffer-Heeger的拓扑和拓扑超导体相，并给出它们的相图。