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We study the effects of electron-electron interactions on the chargeexcitation spectrum of the spinful Su-Schrieffer-Heeger (SSH) model, aprototype of a 1D bulk obstructed topological insulator. In view of recentprogress in the fabrication of dopant-based quantum simulators we focus onexperimentally detectable signatures of interacting topology in finitelattices. To this end we use Lanczos-based exact diagonalization to calculatethe single-particle spectral function in real space which generalizes the localdensity of states to interacting systems. Its spatial and spectral resolutionallows for the direct investigation and identification of edge states. Bystudying the non-interacting limit, we demonstrate that the topological in-gapstates on the boundary are robust against both finite-size effects as well asrandom bond and onsite disorder which suggests the feasibility of simulatingthe SSH model in engineered dopant arrays in silicon. While edge excitationsbecome zero-energy spin-like for any finite interaction strength, our analysisof the spectral function shows that the single-particle charge excitations aregapped out on the boundary. Despite the loss of topological protection we findthat these edge excitations are quasiparticle-like as long as they remainwithin the bulk gap. Above a critical interaction strength of $U_c\approx 5 t$these quasiparticles on the boundary loose their coherence which is explainedby the merging of edge and bulk states. This is in contrast to the many-bodyedge excitations which survive the limit of strong coupling, as established inthe literature. Our findings show that for moderate repulsive interactions thenon-trivial phase of the interacting SSH model can be detected through remnantsignatures of topological single-particle states using single-particle localmeasurement techniques such as scanning tunneling spectroscopy.

Quasiparticle excitations in a one-dimensional interacting topological insulator: Application for dopant-based quantum simulation