Majorana zero modes and long range edge correlation in interacting Kitaev chains: analytic solutions and density-matrix-renormalization-group study

We study the interacting Kitaev chain model with open boundary condition by using exact analytic methods as well as using density-matrix-renormalization-group (DMRG) method. At the symmetry point △=t and zero chemical potential, the interacting model is mapped onto a noninteracting fermion model by applying two Jordan-Wigner transformations and a spin rotation and is diagonalized exactly. For generic parameters, we resort to DMRG to study the model. We suggest and examine an edge correlation function of Majorana fermions to characterize the long range order in the topological superconducting states and study the phase diagram of the interating Kitaev chain.