Determine when insulating ensembles enter collectively correlated phases

Determine a general condition under which the insulating molecular ensemble with finite occupation of the collectively degenerate electronic subspace enters a collectively correlated phase, characterized by nonzero correlation free energy.

Background

The paper distinguishes a metallic mechanism, for which the free-energy condition f(T,σ₀) < −Δᵢₒ determines entry into a collectively correlated phase, from an insulating mechanism in which the occupation number remains finite.

For the insulating case, the authors explicitly state that no generic criterion is known for whether the correlation free energy can become nonzero. Establishing such a criterion would determine when cavity-mediated transverse electron correlations arise without producing metallic behavior.

References

In contrast, for the insulating case (see Fig. \ref{fig:setup}), no generic condition is currently known for entering the collectively correlated phases, i.e., whether $F_{\rm corr}(T,\sigma_0)\neq 0$ is achievable.

— Evidence for cavity-induced metallic phase from entropic electron correlation effects  (2608.16593 - Horak et al., 17 Aug 2026) in Section discussing the simplified two-level model and phase diagram, immediately before the external-field calculation

Furthermore, we cannot make any statement about the number density of these collectively ionized orbitals.

— Evidence for cavity-induced metallic phase from entropic electron correlation effects  (2608.16593 - Horak et al., 17 Aug 2026) in Metallic case, paragraph following Eq. (\ref{eq:metallic})