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An ensemble Green's function formalism, based on the von Neumann densitymatrix approach, to calculate one-electron excitation spectra of amany-electron system with degenerate ground states is proposed. A set ofiterative equations for the ensemble Green's function and self-energy isderived and a simplest approximation corresponding to an ensemble $GW$approximation is naturally obtained. The derivation is based on the Schwingerfunctional derivative technique and does not assume any adiabatic connectionbetween a noninteracting and an interacting ground state.

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