  We study Kitaev model in one-dimension with open boundary condition by using
exact analytic methods for non-interacting system at zero chemical potential as
well as in the symmetric case of {\Delta} = t, and by using
density-matrix-renormalizationgroup method for interacting system with nearest
neighbor repulsion interaction. 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.
