Test the conjectured generality of boson-exchange instabilities in realistic systems

Establish whether instability regions qualitatively similar to those found in the Hubbard atom and zero-point model occur in more realistic strongly coupled systems, including the lattice Hubbard model, when exact noniterated inputs are replaced by dynamical mean-field theory or cluster-dynamical mean-field theory inputs.

Background

The Hubbard atom and zero-point model exhibit qualitatively similar instability structures across TRILEX, SBE, and MBE calculations. On this basis, the authors formulate a conjecture that analogous instabilities will arise in more realistic applications, such as lattice Hubbard models and diagrammatic extensions of DMFT. This remains unresolved because the paper does not perform the corresponding realistic lattice calculations.

References

Such an essential agreement in the stability features of these two intrinsically different models leads us to conjecture that correspondingly similar situations will occur, mutatis mutandis, when applying these diagrammatic approaches to more realistic cases (such as, e.g., the lattice Hubbard model) in their strong-coupling regimes [e.g., by replacing the exact input currently used in the diagrammatic schemes with a \mbox{(cluster-)}DMFT input].

— Instabilities in self-consistent diagrammatic approaches and how to cure them  (2609.11405 - Gievers et al., 10 Sep 2026) in Section 5.1, Consequences for practical calculations