Ensemble Green’s function theory for interacting electrons with degenerate ground states

In nature, correlated electronic systems containing degenerate ground states are common, with the degeneracy leading to fascinating phenomena such as the quantum Hall effect and emergent magnetic monopoles. Application of the Green’s function theory to degenerate systems has however not been extensively considered, in part stemming from the adiabatic connection being ambiguous for degenerate states. Current approaches either ignore the degeneracy or incorporate it in a non-generalizable manner. In our work [Phys. Rev. B 100, 235106 (2019)] we propose an ensemble Green’s function formalism, based on the von Neumann density matrix approach, for treating the one-electron excitation spectra of a degenerate electronic system. In the spirit of Hedin, we derive a set of iterative equations for the ensemble Green’s function and self-energy, and propose an 'ensemble GW' approximation, allowing for a well-defined treatment of degenerate electronic systems. The aim is to present the issues of degeneracy within the standard Green’s function method with focus on our proposed ensemble Green’s function method.