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We study Kitaev model in one-dimension with open boundary condition by usingexact analytic methods for non-interacting system at zero chemical potential aswell as in the symmetric case of {\Delta} = t, and by usingdensity-matrix-renormalizationgroup method for interacting system with nearestneighbor repulsion interaction. We suggest and examine an edge correlationfunction of Majorana fermions to characterize the long range order in thetopological superconducting states and study the phase diagram of theinterating Kitaev chain.

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