Gor'kov-Hedin-Baym Equations for Quantum Many-Body Systems with Spin-Dependent Interactions

TL;DR

This paper extends the Gor'kov-Hedin-Baym equations to include spin-dependent interactions, enabling better modeling of complex superconducting materials with multiple correlated effects.

Contribution

It introduces a generalized set of self-consistent equations incorporating spin-dependent electron-electron and electron-phonon interactions for quantum many-body systems.

Findings

Generalizes Migdal-Eliashberg theory for spin-dependent interactions

Derives a framework for including relativistic effects in superconductivity models

Enables natural emergence of ladder vertex corrections in calculations

Abstract

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.