Source of negative spectral weights in HF-eGKBA

Determine whether the nonstandard equation structure G = G_HF + G_HFΣG_HF in the Hartree–Fock extended Generalized Kadanoff–Baym Ansatz is the main source of negative spectral weights.

Background

The paper studies the Hartree–Fock extended Generalized Kadanoff–Baym Ansatz (HF-eGKBA), in which the retarded Green’s function satisfies a relation of the form G = G_HF + G_HFΣG_HF rather than the usual Dyson equation G = G_HF + G_HFΣG. Numerical calculations for a six-site Hubbard ring show that the HF-eGKBA spectral function becomes negative at sufficiently strong interaction strengths.

The paper relates these negative spectral features to previously observed negative densities and instabilities in standard Hartree–Fock GKBA calculations. It reports that replacing the nonstandard equation with one having the usual Dyson structure eliminates the negative spectral functions in the model considered, but the underlying causal mechanism is presented as a conjecture rather than established conclusively.

References

A physical free-carrier population created by exciton--exciton scattering at these densities cannot be excluded at the present level, but would not be represented differently by the mean-field reconstruction.

— Real-time Dyson expansion for the nonequilibrium $GW$ approximation: Correlated spectra and dependence on the reference propagator  (2609.08932 - Schroedter et al., 8 Sep 2026) in Section 5.4.1, “Excitonic replica”

As conjectured in Ref., the main source of negative spectral weights is the structure of Eq.$~$gkbagra_aux, i.e., $G=G_{HF}+G_{HF}\Sigma G_{HF}$, which is not the standard structure of the Dyson equation.

gkbagra_aux:

GR(ω,k)=GHFR(ω,k)+GHFR(ω,k)ΣR(ω,k)GHFR(ω,k)G^{R}(\omega,k)=G^{R}_{HF}(\omega,k) + G^{R}_{HF}(\omega,k)\Sigma^{R}(\omega,k) G^{R}_{HF}(\omega,k)

— On spectral properties of Generalized Kadanoff--Baym Ansatz  (2609.09067 - Hopjan, 8 Sep 2026) in Section Discussion