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

## TL;DR

This paper introduces an ensemble Green's function formalism using the von Neumann density matrix to accurately compute excitation spectra in many-electron systems with degenerate ground states, extending existing methods.

## Contribution

It develops a novel ensemble Green's function approach based on the von Neumann density matrix, including iterative equations and an ensemble GW approximation, without adiabatic assumptions.

## Key findings

- Derived a set of iterative equations for ensemble Green's function and self-energy.
- Established a natural ensemble GW approximation within the formalism.
- Provided a method applicable to systems with degenerate ground states.

## Abstract

An ensemble Green's function formalism, based on the von Neumann density matrix approach, to calculate one-electron excitation spectra of a many-electron system with degenerate ground states is proposed. A set of iterative equations for the ensemble Green's function and self-energy is derived and a simplest approximation corresponding to an ensemble $GW$ approximation is naturally obtained. The derivation is based on the Schwinger functional derivative technique and does not assume any adiabatic connection between a noninteracting and an interacting ground state.