Topological phase transition in an $sp$- orbital chain

We study an $sp$- orbital chain. The existence of edge states is discovered for this system. The quantum phases of the chain filled with fermions (half filling) are studied with exact diagonalization. We find a topological phase of fermions with edge states occupied. The topological phase is robust against small interactions. With sufficiently strong interaction the fermion system undergoes a topological phase transition to a inter-chain paired phase.