Persistence of flat-envelope coexistence with nonzero correlation corrections

Determine whether the coexistence of an exactly flat smooth envelope and a nonzero correlation correction g persists in interacting systems, and identify the corresponding interacting-system quantity g^{(2)}.

Background

In the random free-fermion ensemble, the smooth function f_{11}2 is energy independent while the correlation correction g_{11} is nonzero and of order one. This demonstrates that a flat ETH envelope does not imply microscopic decorrelation.

The paper leaves unresolved whether this coexistence survives after interactions are introduced and how the relevant second-order hierarchy contribution should be defined or identified in that setting.

References

What remains open is whether that coexistence persists in interacting systems, and how the corresponding $g{(2)}$ is to be identified.

— Eigenstate thermalization beyond the envelope: exact two-point overlap statistics in random free fermions  (2609.17037 - Huang, 15 Sep 2026) in Section 6, Discussion, paragraph beginning “Three features of the bridge to the framework are worth recording”