Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1805.06802 · The European Physical Journal B

Local vertex corrections from exchange-correlation kernels with a discontinuity

Maria Hellgren

Published Jul 1, 2018• 5 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2018-90110-1

Related papers

Local and non-local vertex corrections in GW for extended and localized systems

Martin Stankovski, Andrew J. Morris, Benjamin Robinson +6 more

Bulletin of the American Physical Society•Mar 8, 2007•0 citations

The Lieb-Oxfourd bound and the exchange-correlation kernel from the strictly-correlated electrons functional

Paola Gori‐Giorgi

Bulletin of the American Physical Society•Mar 14, 2016•0 citations

Dynamical exchange-correlation potentials beyond the local density approximation

Jianmin Tao, Giovanni Vignale

Bulletin of the American Physical Society•Mar 14, 2006•0 citations

Parametrizations of local vertex corrections from weak to strong coupling: Importance of the Hedin three-leg vertex

Viktor Harkov, Alexander I. Lichtenstein, Friedrich Krien

In the study of correlated systems, approximations based on the dynamical mean-field theory (DMFT) provide a practical way to take local vertex corrections into account, which capture, respectively, particle-particle screening at weak coupling and the formation of the local moment at strong coupling. We show that in both limits the local vertex corrections can be efficiently parametrized in terms of single-boson exchange, such that the two-particle physics described by DMFT and its diagrammatic extensions is recovered to good approximation and at a reduced computational cost. Our investigation highlights the importance of the frequency-dependent fermion-boson coupling (Hedin vertex) for local vertex corrections. Namely, at weak coupling the fermion--spin-boson coupling suppresses the N\'eel temperature of the DMFT approximation compared with the static mean field, whereas for large interaction it facilitates a huge enhancement of local spin-fluctuation exchange, giving rise to the effective-exchange energy scale $4{t}^{2}/U$. We find that parametrizations of the vertex which neglect the nontrivial part of the fermion-boson coupling fail qualitatively at strong coupling.

arXiv:2104.11534•Physical review. B./Physical review. B•Sep 27, 2021•26 citations

Parameterizations of local vertex corrections from weak to strong coupling: importance of the Hedin three-leg vertex

Viktor Harkov, Alexander I. Lichtenstein, Friedrich Krien

In the study of correlated systems, approximations based on the dynamical mean-field theory (DMFT) provide a practical way to take local vertex corrections into account, which capture, respectively, particle-particle screening at weak coupling and the formation of the local moment at strong coupling. We show that in both limits the local vertex corrections can be efficiently parameterized in terms of single-boson exchange, such that the two-particle physics described by DMFT and its diagrammatic extensions is recovered to good approximation and at a reduced computational cost. Our investigation highlights the importance of the frequency-dependent fermion-boson coupling (Hedin vertex) for local vertex corrections. Namely, at weak coupling the fermion-spin-boson coupling suppresses the N\'eel temperature of the DMFT approximation compared to the static mean-field, whereas for large interaction it facilitates a huge enhancement of local spin-fluctuation exchange, giving rise to the effective-exchange energy scale $4t^2/U$. We find that parameterizations of the vertex which neglect the nontrivial part of the fermion-boson coupling fail qualitatively at strong coupling.

•Apr 23, 2021•0 citations

Vertex function compliant with the Ward identity for quasiparticle self-consistent calculations beyond GW

Alexey A. Tal, Wei Chen, Alfredo Pasquarello

We extend the quasiparticle self-consistent approach beyond the $GW$ approximation by using a range-separated vertex function. The developed approach yields band gaps, dielectric constants, and band positions with an accuracy similar to highest-level electronic-structure calculations without exceeding the cost of regular quasiparticle self-consistent $GW$. We introduce an exchange-correlation kernel that accounts for the vertex over the full spatial range. In the long range it complies with the Ward identity, while it is approximated through the adiabatic local density functional in the short range. In this approach, the renormalization factor is balanced and the higher-order diagrams are effectively taken into account.

Physical review. B./Physical review. B•Apr 8, 2021•33 citations
In the study of correlated systems, approximations based on the dynamical mean-field theory (DMFT) provide a practical way to take local vertex corrections into account, which capture, respectively, particle-particle screening at weak coupling and the formation of the local moment at strong coupling. We show that in both limits the local vertex corrections can be efficiently parametrized in terms of single-boson exchange, such that the two-particle physics described by DMFT and its diagrammatic extensions is recovered to good approximation and at a reduced computational cost. Our investigation highlights the importance of the frequency-dependent fermion-boson coupling (Hedin vertex) for local vertex corrections. Namely, at weak coupling the fermion--spin-boson coupling suppresses the N\'eel temperature of the DMFT approximation compared with the static mean field, whereas for large interaction it facilitates a huge enhancement of local spin-fluctuation exchange, giving rise to the effective-exchange energy scale 4t2/U4{t}^{2}/U4t2/U. We find that parametrizations of the vertex which neglect the nontrivial part of the fermion-boson coupling fail qualitatively at strong coupling.
In the study of correlated systems, approximations based on the dynamical mean-field theory (DMFT) provide a practical way to take local vertex corrections into account, which capture, respectively, particle-particle screening at weak coupling and the formation of the local moment at strong coupling. We show that in both limits the local vertex corrections can be efficiently parameterized in terms of single-boson exchange, such that the two-particle physics described by DMFT and its diagrammatic extensions is recovered to good approximation and at a reduced computational cost. Our investigation highlights the importance of the frequency-dependent fermion-boson coupling (Hedin vertex) for local vertex corrections. Namely, at weak coupling the fermion-spin-boson coupling suppresses the N\'eel temperature of the DMFT approximation compared to the static mean-field, whereas for large interaction it facilitates a huge enhancement of local spin-fluctuation exchange, giving rise to the effective-exchange energy scale 4t2/U4t^2/U4t2/U. We find that parameterizations of the vertex which neglect the nontrivial part of the fermion-boson coupling fail qualitatively at strong coupling.
We extend the quasiparticle self-consistent approach beyond the GWGWGW approximation by using a range-separated vertex function. The developed approach yields band gaps, dielectric constants, and band positions with an accuracy similar to highest-level electronic-structure calculations without exceeding the cost of regular quasiparticle self-consistent GWGWGW. We introduce an exchange-correlation kernel that accounts for the vertex over the full spatial range. In the long range it complies with the Ward identity, while it is approximated through the adiabatic local density functional in the short range. In this approach, the renormalization factor is balanced and the higher-order diagrams are effectively taken into account.