  The one dimension interacting Kitaev chain at half filling is studied. The
symmetry of the Hamiltonian is examined by dual transformations and various
physical quantities as functions of the fermion-fermion interaction $U$ are
calculated systematically using the density matrix renormalization group
method. A special value of interaction $U_p$ is revealed in the topological
region of the phase diagram. We show that at $U_p$ the ground states are
strictly two-fold degenerate even though the chain length is finite and the
zero-energy peak due to the Majorana zero modes is maximally enhanced and
exactly localized at the end sites. $U_p$ may be attractive or repulsive
depending on other system parameters. We also give a qualitative understanding
of the effect of interaction under the self-consistent mean field framework.
