Probing boundary spins in the Su-Schrieffer-Heeger-Hubbard model

Studying boundary excitations provides a powerful approach to probe correlations in topological phases. We propose that localized spins near the ends of a Su--Schrieffer--Heeger--Hubbard chain embedded in an insulating environment can be detected experimentally using scanning tunneling microscopy (STM) combined with electron-spin resonance. When the STM tip is in the contact regime, the tip--end-spin coupling realizes an effective Anderson impurity problem, giving rise to a Kondo peak at low bias. Spatially resolving the Kondo resonance width as the STM tip approaches the chain ends provides an indirect yet clear signature of these localized spins. To support this proposal, we use density-matrix renormalization group (DMRG) to calculate the spin gap and spin projection of end states for chains of various lengths and interaction strengths $U$ at half filling. In the noninteracting limit ($U=0$), we derive simple analytical expressions that reproduce the numerical results for sufficiently long chains. We also discuss how the correlated phase of the isolated chain is characterized by boundary zeros in its single-particle Green's function, and briefly comment on their localization properties in relation to the boundary spins.