Effect of Interaction on the Majorana Zero Modes in the Kitaev Chain at Half Filling

The one-dimensional interacting Kitaev chain at half filling is studied. The symmetry of the Hamiltonian is examined by dual transformations, and various physical quantities as a function of the fermion-fermion interaction U are calculated systematically using the density matrix renormalization group method. A special value of interaction U_\rm p is revealed in the topological region of the phase diagram. We show that at U_\rm 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. Here U_\rm 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.