  We investigate in a fully quantum-mechanical manner how the many-body
excitation spectrum of topological insulators is affected by the presence of
long-range Coulomb interactions. In the one-dimensional Su-Schrieffer-Heeger
model and its mirror-symmetric variant strongly localized plasmonic excitations
are observed which originate from topologically non-trivial single-particle
states. These \textit{"topological plasmons"} inherit some of the
characteristics of their constituent topological single-particle states, but
they are not equally well protected against disorder due to the admixture of
non-topological bulk single-particle states in the polarization function. The
strength of the effective Coulomb interactions is also shown to have strong
effects on the plasmonic modes. Furthermore, we show how external modifications
via dielectric screening and applied electric fields with distinct symmetries
can be used to study topological plasmons, thus allowing for experimental
verification of our atomistic predictions.
