Role of dispersive optical phonons in the one-dimensional doped Hubbard-Su-Schrieffer-Heeger model.

Electron-phonon (e-ph) interactions play a crucial role in determining many properties of strongly correlated systems. In this context, the Su-Schrieffer-Heeger (SSH) model, where atomic motion modulates the electronic hopping, has gained significant attention due to its potential for strong electron pairing and possible high-Tc superconductivity. Previous studies of the Hubbard-SSH (HSSH) model have highlighted several important properties, but mostly focused on the dilute or half-filled limits with Einstein (dispersionless) phonons. In our study, however, we observe the effects of dispersive optical phonons on the moderately doped HSSH model using the density matrix renormalization group (DMRG) method. We find a significant enhancement in the pairing of electrons driven by the phonon bandwidth. The pairing is manifested as a pronounced spin gap in the system, which can be measured experimentally. However, by obtaining various correlation functions, we find that the enhanced pairing does not translate to superconducting correlations in the studied parameter regime. Nevertheless, the significant impact of phonon dispersion on our results indicates the necessity to go beyond the Einstein phonon limit in the modeling of realistic quantum materials.