Downfolding the Su-Schrieffer-Heeger model

Charge-density waves are responsible for symmetry-breaking displacements of atoms and concomitant changes in the electronic structure. Linear response theories, particular density-functional perturbation theory, provide a way to study effect on both total energy structure based single ab initio calculation. In downfolding approaches, system is reduced smaller number bands, allowing incorporation additional correlation environmental effects these bands. However, physical contents this downfolded model its potential limitations not always obvious. Here, we potential-energy landscape Su-Schrieffer-Heeger (SSH) model, where all relevant quantities can be evaluated analytically. We compare exact results at arbitrary displacement with diagrammatic theory full effective single-band which gives an instructive insight into properties downfolding. An reconstruction possible requires dynamical electron-biphonon interaction. The dispersion bands upon atomic also found correctly, by construction only captures spectral weight target space. SSH electron-phonon coupling mechanism involves exclusively hybridization between low- high-energy limits computational efficiency gain models.