Ensemble Green's Function Theory for Interacting Electrons with Degenerate Ground States

Abstract: An ensemble Green's function theory for many-electron systems with degenerate ground states, based on the von Neumann density matrix formalism, is proposed. The formalism is constructed without an assumption of an adiabatic connection. An ensemble analogue of Hedin's equations and the GW Approximation (GWA) is constructed. The formalism is applied to four model systems within GWA: a three-orbital Hubbard model, a two-dimensional harmonic oscillator, an Ising model with a triangular lattice and a hydrogen-like system, with comparison to the exact solutions. The response function and the Green's function are found to be in reasonable agreement with the exact result for the majority of the models. However, peaks originating from the non-interacting degenerate subspace are found to be routinely neglected in the response function by our employed one-shot computational approach. Furthermore, the relation between the finite-temperature Green's function theory and the proposed theory is studied, and an extension of the finite-temperature formalism to include electronic systems with degenerate states is proposed.