Generalized Hedin equations and σGσW approximation for quantum many-body systems with spin-dependent interactions

The Hedin equations for the electron self-energy and the vertex were originally derived for a many-electron system with Coulomb interaction (Hedin 1965 Phys. Rev. 139 A796). Here, we present a generalized set of Hedin equations for quantum many-body systems containing spin-dependent interactions, e.g. spin-orbit and spin-spin interactions. The corresponding spin-dependent GW approximation is constructed. This work should open the way to describing the interplay of correlations and spin-dependent interactions in systems such as quantum dots or wires, as well as in interface and surface problems.