  The fermionic and bosonic zero modes of the 1D interacting Kitaev chain at
the symmetric point are unveiled. The many-body structures of the Majorana zero
modes in the topological region are given explicitly by carrying out
perturbation expansion up to infinite order. We also give the analytic
expressions of the bosonic zero modes in the topologically trivial phase. Our
results are generalized to the hybrid fermion system comprised of the
interacting Kitaev model and the Su-Schrieffer-Heeger model, in which we show
that these two types of zero modes can coexist in certain region of its phase
diagram.
