  We study a one-dimensional interacting topological model by means of exact
diagonalization method. The topological properties are firstly examined with
the existence of the edge states at half-filling. We find that the topological
phases are not only robust to small repulsive interactions but also are
stabilized by small attractive interactions, and also finite repulsive
interaction can drive a topological non-trivial phase into a trivial one while
the attractive interaction can drive a trivial phase into a non-trivial one.
Next we calculate the Berry phase and parity of the bulk system and find that
they are equivalent in characterizing the topological phases. With them we
obtain the critical interaction strengths and construct part of the phase
diagram in the parameters space. Finally we discuss the effective Hamiltonian
at large-U limit and provide additional understanding of the numerical results.
Our these results could be realized experimentally using cold atoms trapped in
the 1D optical lattice.
