Downfolding the Su-Schrieffer-Heeger model

TL;DR

This paper analytically investigates the downfolding of the SSH model, demonstrating how a single-band effective model can accurately reproduce the potential energy landscape and electronic structure, with insights into its limitations.

Contribution

It provides an analytical comparison between the full SSH model and a downfolded single-band model, clarifying the physical content and limitations of downfolding techniques.

Findings

Exact potential-energy landscape reconstruction is possible with a dynamical electron-biphonon interaction.

Downfolded model correctly captures band dispersion upon displacement.

Electron-phonon coupling involves hybridization, limiting efficiency gains.

Abstract

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