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Downfolding the Su-Schrieffer-Heeger model

by Arne Schobert, Jan Berges, Tim Wehling, Erik van Loon

Submission summary

As Contributors: Erik van Loon
Arxiv Link: https://arxiv.org/abs/2104.09207v2 (pdf)
Date submitted: 2021-05-11 11:07
Submitted by: van Loon, Erik
Submitted to: SciPost Physics
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approach: Theoretical

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.

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Submission 2104.09207v2 on 11 May 2021

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