Determine the precise convex-Gaussian temperature threshold

Determine the precise inverse-temperature threshold at which Gibbs states of interacting fermionic Hamiltonians become convex-Gaussian.

Background

The paper studies sufficient inverse-temperature windows guaranteeing convex-Gaussianity for weakly perturbed quadratic fermionic Hamiltonians and for the strong-coupling Fermi–Hubbard model. Although these results establish scaling laws and asymptotic tightness in the weak-coupling setting, they do not characterize the exact temperature threshold for general interacting fermionic systems. The authors identify determining that threshold as an unresolved problem.

References

However, determining the precise temperature threshold at which this property holds remains a non-trivial problem.

— Convex-Gaussianity of fermionic Gibbs states in perturbation theory  (2609.09608 - Bu et al., 9 Sep 2026) in Section 1, Introduction