Effect of interaction in one-dimensional topological insulator

The one-dimensional interacting topological insulator is studied by means of exact diagonalization method. The topological properties are examined with the existence of the edge states and the quantized berry phase at half-filling. It is found 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 nontrivial phase into a trivial one while the attractive interaction can drive a trivial phase into a nontrivial one. These results could be realized experimentally using cold atoms trapped in the 1D optical lattice.