  Recently topogical excitons have attracted much attention. However, studies
on the topological properties of excitons in one dimension are still rare. Here
we have computed the Zak phase for a generic one-dimensional dimerised
excitonic model. Tuning relevant hopping parameters gives rise to a rich
spectrum of physics, including non-trivial topological phase in uniform chain
unlike the conventional Su-Shcrieffer-Heeger model, topologically nontrivial
flat bands, and exotic fractional phase. a new concept of ``composite chiral
site" was developed to interpret the Zak phase of $\pi$ in our calculations.
Our finite-chain calculations substantiate topological edge states, providing
more information about their characteristics. Most importantly, in the first
time, a topological phase transition assisted by the Dexter electron exchange
process has been found.
