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:0708.4058 · Physical Review Letters

Generalized Hedin’s Equations for Quantum Many-Body Systems with Spin-Dependent Interactions

F. Aryasetiawan, Silke Biermann

Published Mar 19, 2008• 77 citations
arXivHTMLPDF

Abstract

Hedin's equations for the electron self-energy and the vertex have originally been derived for a many-electron system with Coulomb interaction. In recent years, it has been increasingly recognized that spin interactions can play a major role in determining physical properties of systems such as nanoscale magnets or of interfaces and surfaces. We derive a generalized set of Hedin's equations for quantum many-body systems containing spin interactions, e.g., spin-orbit and spin-spin interactions. The corresponding spin-dependent GW approximation is constructed.

DOI
10.1103/physrevlett.100.116402

Related papers

Gor'kov-Hedin-Baym equations for quantum many-body systems with spin-dependent interactions

Christopher Lane

Driven by the need to understand and determine the presence of non-trivial superconductivity in real candidate materials, we present a generalized set of self-consistent Gor'kov-Hedin-Baym equations with spin dependent electron-electron and electron-phonon interactions. This extends Hedin's original equations to treat quantum many-body systems where electronic and lattice correlations along with relativistic effects coexist on the same footing with superconductivity. The leading order self-energies yields a generalization of the Migdal-Eliashberg theory and by iterating this set of equations generalized ladder vertex corrections naturally emerge.

arXiv:2506.07302•Physical review. B./Physical review. B•Mar 20, 2026•1 citation

Hedin Equations for Superconductors

A. Linscheid, F. Essenberger

We generalize Hedin equations to a system of superconducting electrons coupled with a system of phonons. The electrons are described by an electronic Pauli Hamiltonian which includes the Coulomb interaction among electrons and an external vector and scalar potential. We derive the continuity equation in the presence of the superconducting condensate and point out how to cast vertex corrections in the form of a non-local effective interaction that can be used to describe both fluctuations of spin and superconducting phase beyond the screened Coulomb self-energy diagram.

arXiv:1503.00970•Mar 3, 2015•1 citation

Hedin Equations, GW, GW+DMFT, and All That

Karsten Held, Ciro Taranto, G. Rohringer +1 more

Historically, the GW approach was put forward by Hedin as the simplest approximation to the so-called Hedin equations. In Section 2, we will derive these Hedin equations from a Feynman-diagrammatical point of view. Section 3.1 shows how GW arises as an approximation to the Hedin equations. In Section 3.2, we briefly present some typical GW results for materials, including quasiparticle renormalizations, lifetimes, and band gap enhancements. In Section 4, the combination of GW and DMFT is summarized. Finally, as a prospective outlook, ab initio dynamical vertex approximation D$Γ$A is introduced in Section 5 as a unifying scheme for all that: GW, DMFT and non-local vertex correlations beyond.

arXiv:1109.3972•Sep 19, 2011•8 citations

Hedin’s equations and enumeration of Feynman diagrams

Luca Guido Molinari

Hedin's equations are solved perturbatively in zero dimension to count Feynman graphs for self-energy, polarization, propagator, effective potential and vertex function in a many-body theory of fermions with two-body interaction. Counting numbers are also obtained in the $GW$ approximation.

arXiv:cond-mat/0401500•Physical Review B•Mar 17, 2005•25 citations

Quantum field theory of electrons and nuclei

Ville J. Härkönen

Abstract We develop a non-relativistic quantum field theory of electrons and nuclei with Coulomb interactions. We derive the exact equations of motion and write these equations in the form of Hedin’s equations for all species of identical particles involved. Theory derived allows the computation of exact observables and provides a rigorous starting point to derive approximations in a systematic way.

arXiv:2403.16103•Journal of Physics A Mathematical and Theoretical•Oct 22, 2024•5 citations

Many-Electron Green Function

F. Aryasetiawan, Fredrik Nilsson

In this chapter, a summary of the main properties of the many-electron Green function, which is a central quantity in many-electron theory, is given. The physical interpretation of the Green function and its connection to the experiment are described. Hedin's equations as a set of iterative equations determining the self-energy, and hence the Green function, are derived. Linear response theory and the screened interaction underlying the self-energy formalism are elucidated in detail. Finally, we also describe the thermal (Matsubara) Green function that can be used to describe systems at finite temperatures.

•Aug 3, 2022•0 citations
Hedin's equations for the electron self-energy and the vertex have originally been derived for a many-electron system with Coulomb interaction. In recent years, it has been increasingly recognized that spin interactions can play a major role in determining physical properties of systems such as nanoscale magnets or of interfaces and surfaces. We derive a generalized set of Hedin's equations for quantum many-body systems containing spin interactions, e.g., spin-orbit and spin-spin interactions. The corresponding spin-dependent GW approximation is constructed.
Driven by the need to understand and determine the presence of non-trivial superconductivity in real candidate materials, we present a generalized set of self-consistent Gor'kov-Hedin-Baym equations with spin dependent electron-electron and electron-phonon interactions. This extends Hedin's original equations to treat quantum many-body systems where electronic and lattice correlations along with relativistic effects coexist on the same footing with superconductivity. The leading order self-energies yields a generalization of the Migdal-Eliashberg theory and by iterating this set of equations generalized ladder vertex corrections naturally emerge.
We generalize Hedin equations to a system of superconducting electrons coupled with a system of phonons. The electrons are described by an electronic Pauli Hamiltonian which includes the Coulomb interaction among electrons and an external vector and scalar potential. We derive the continuity equation in the presence of the superconducting condensate and point out how to cast vertex corrections in the form of a non-local effective interaction that can be used to describe both fluctuations of spin and superconducting phase beyond the screened Coulomb self-energy diagram.
Historically, the GW approach was put forward by Hedin as the simplest approximation to the so-called Hedin equations. In Section 2, we will derive these Hedin equations from a Feynman-diagrammatical point of view. Section 3.1 shows how GW arises as an approximation to the Hedin equations. In Section 3.2, we briefly present some typical GW results for materials, including quasiparticle renormalizations, lifetimes, and band gap enhancements. In Section 4, the combination of GW and DMFT is summarized. Finally, as a prospective outlook, ab initio dynamical vertex approximation DΓΓΓA is introduced in Section 5 as a unifying scheme for all that: GW, DMFT and non-local vertex correlations beyond.
Hedin's equations are solved perturbatively in zero dimension to count Feynman graphs for self-energy, polarization, propagator, effective potential and vertex function in a many-body theory of fermions with two-body interaction. Counting numbers are also obtained in the GWGWGW approximation.
In this chapter, a summary of the main properties of the many-electron Green function, which is a central quantity in many-electron theory, is given. The physical interpretation of the Green function and its connection to the experiment are described. Hedin's equations as a set of iterative equations determining the self-energy, and hence the Green function, are derived. Linear response theory and the screened interaction underlying the self-energy formalism are elucidated in detail. Finally, we also describe the thermal (Matsubara) Green function that can be used to describe systems at finite temperatures.