The accuracy of the many-body perturbation theory $GW$ formalism to calculate electron-phonon coupling matrix elements has been recently demonstrated in the case of a few important systems. However, the related computational costs are high and thus represent strong limitations to its widespread application. In the present study, we explore two less demanding alternatives for the calculation of electron-phonon coupling matrix elements on the many-body perturbation theory level. Namely, we test the accuracy of the static Coulomb-hole plus screened-exchange (COHSEX) approximation and further of the constant screening approach, where variations of the screened Coulomb potential $W$ upon small changes of the atomic positions along the vibrational eigenmodes are neglected. We find this latter approximation to be the most reliable, whereas the static COHSEX ansatz leads to substantial errors. Our conclusions are validated in a few paradigmatic cases: diamond, graphene, and the ${\text{C}}_{60}$ fullerene. These findings open the way for combining the present many-body perturbation approach with efficient linear-response theories.The accuracy of the many-body perturbation theory $GW$ formalism to calculate electron-phonon coupling matrix elements has been recently demonstrated in the case of a few important systems. However, the related computational costs are high and thus represent strong limitations to its widespread application. In the present study, we explore two less demanding alternatives for the calculation of electron-phonon coupling matrix elements on the many-body perturbation theory level. Namely, we test the accuracy of the static Coulomb-hole plus screened-exchange (COHSEX) approximation and further of the constant screening approach, where variations of the screened Coulomb potential $W$ upon small changes of the atomic positions along the vibrational eigenmodes are neglected. We find this latter approximation to be the most reliable, whereas the static COHSEX ansatz leads to substantial errors. Our conclusions are validated in a few paradigmatic cases: diamond, graphene, and the ${\text{C}}_{60}$ fullerene. These findings open the way for combining the present many-body perturbation approach with efficient linear-response theories.

arXiv:1501.07058Physical Review BApr 8, 201546 citations

Spectral function of electron-phonon models by cluster perturbation theory

Martin Hohenadler, Markus Aichhorn, Wolfgang von der Linden

Cluster perturbation theory in combination with the Lanczos method is used to compute the one-electron spectral function of the Holstein polaron in one and two dimensions. It is shown that the method allows reliable calculations using relatively small clusters, and at the same time significantly reduces finite-size effects. Results are compared with exact data and the relation to existing work is discussed. We also use a strong-coupling perturbation theory---equivalent to the Hubbard I approximation---to calculate the spectral function of the quarter-filled Holstein model of spinless fermions, starting from the exact atomic-limit Green function. The results agree well with previous calculations within the many-body coherent potential approximation.Cluster perturbation theory in combination with the Lanczos method is used to compute the one-electron spectral function of the Holstein polaron in one and two dimensions. It is shown that the method allows reliable calculations using relatively small clusters, and at the same time significantly reduces finite-size effects. Results are compared with exact data and the relation to existing work is discussed. We also use a strong-coupling perturbation theory---equivalent to the Hubbard I approximation---to calculate the spectral function of the quarter-filled Holstein model of spinless fermions, starting from the exact atomic-limit Green function. The results agree well with previous calculations within the many-body coherent potential approximation.

arXiv:cond-mat/0306740Physical review. B, Condensed matterNov 19, 200356 citations

Renormalization Group Approaches for Systems with Electron-Electron and Electron-Phonon Interactions

Alex C. Hewson, D. Meyer

Springer eBooksJan 1, 20031 citation

The accuracy of the many-body perturbation theory

GW

formalism to calculate electron-phonon coupling matrix elements has been recently demonstrated in the case of a few important systems. However, the related computational costs are high and thus represent strong limitations to its widespread application. In the present study, we explore two less demanding alternatives for the calculation of electron-phonon coupling matrix elements on the many-body perturbation theory level. Namely, we test the accuracy of the static Coulomb-hole plus screened-exchange (COHSEX) approximation and further of the constant screening approach, where variations of the screened Coulomb potential

W

upon small changes of the atomic positions along the vibrational eigenmodes are neglected. We find this latter approximation to be the most reliable, whereas the static COHSEX ansatz leads to substantial errors. Our conclusions are validated in a few paradigmatic cases: diamond, graphene, and the

{\text{C}}_{60}

fullerene. These findings open the way for combining the present many-body perturbation approach with efficient linear-response theories.