Resolve the low-occupation limit of the quasiparticle-weight parametrization

Develop a more careful parametrization of the quasiparticle weight for the Bethe-lattice Hubbard model in the low-occupation limit n0 so that the i-DFT exchange-correlation bias parameters, particularly 2, vanish appropriately and the resulting spectral function converges to the non-interacting Kohn-Sham spectral function.

Background

The proposed i-DFT exchange-correlation bias functional fails to recover the non-interacting Kohn-Sham spectral function as the density tends to zero. The authors attribute this behavior to their parametrization of the quasiparticle weight Z, which does not approach unity sufficiently rapidly in that limit. Consequently, the factor Z{-2}-1 in the expression for the coefficient 2 does not decay quickly enough to offset the rapidly vanishing fourth power of the Kohn-Sham spectral function at the Fermi level and the divergence of its derivative.

The unresolved task is therefore to construct a more accurate low-density parametrization of Z that makes 2 vanish as required and restores the correct non-interacting limit of the spectral function.

References

In the limit of low occupation, n\to0, the spectral function does not converge to the non-interacting (i.e. the KS) spectral function given by Eq.~(\ref{sf}). Most likely, this is due to our parametrization of the quasiparticle weight not approaching unity fast enough in the limit n\to0. Hence Z{-2}-1 in the numerator of Eq.~(\ref{lambda2}) does not vanish fast enough in the limit n\to0 to compensate both for A_s(0)4 in the denominator going to zero extremely fast as well as for the divergence of A_s\prime(0) in the same limit. This prevents \lambda_2 from vanishing in this limit, as it should. We suspect that the problem can be fixed by a more careful parametrization of Z in this limit.

— Doping-driven Mott transition from steady-state density functional theory  (2608.21029 - Jacob et al., 21 Aug 2026) in Section 4, discussion accompanying Fig. 5 (the paragraph beginning 'Fig.~\\ref{fig:3d_spectra} also shows some limitations')