  We have studied the excited states of a one-dimensional donor dimer array by
using time-dependent Hartree-Fock and density-functional theories. We find that
tuning the inter-donor distances can induce a topological phase transition from
a topologically trivial anti-ferromagnetic ground state to a topological phase
supporting spin-polarised edge states. Significant changes in the optical
spectra accompany this transition, providing signatures for the phase
transition and the existence of the edge state; the edge states lead to a
robust $1s\rightarrow 2p$ atomic transition. By contrast, the bulk of the chain
becomes spinless, inducing a reduction in the HOMO-LUMO gap and a decrease of
the excitation energies in the optical spectra. The inclusion of physics beyond
the Su-Schrieffer-Heeger-Hubbard model (long-range electron correlations and
basis states beyond the 1s manifold) has a critical effect on the results and
leads to the novel prediction of a change in optical response related to a
topological phase transition. Our results provide a theoretical foundation for
using artificial donor linear arrays in semiconductors to form topological edge
states by design.
