Exact solution to an interacting dimerized Kitaev model at symmetric point

We study the interacting dimerized Kitaev chain at the symmetry point $\Delta=t$ and the chemical potential $\mu=0$ under open boundary conditions, which can be exactly solved by applying two Jordan-Wigner transformations and a spin rotation. By using exact analytic methods, we calculate two edge correlation functions of Majorana fermions and demonstrate that they can be used to distinguish different topological phases and characterize the topological phase transitions of the interacting system. According to the thermodynamic limit values of these two edge correlation functions, we give the phase diagram of the interacting system which includes three different topological phases: the trivial, the topological superconductor and the Su-Schrieffer-Heeger-like topological phase and we further distinguish the trivial phase by obtaining the local density distribution numerically.