Develop a non-perturbative theory of chemical observables for infinitely degenerate spin-glass correlations

Develop a fundamental non-perturbative treatment of chemical observables for the infinitely degenerate spherical Sherrington–Kirkpatrick solution describing cavity-mediated electron correlations, in order to connect the spin-glass theory to experiments.

Background

The paper uses a mapping between cavity-mediated transverse electron correlations and the spherical Sherrington–Kirkpatrick spin-glass model. In the thermodynamic limit, the spin-glass solution is infinitely degenerate, which makes the calculation of experimentally relevant local chemical observables nontrivial.

The authors identify the development of a non-perturbative framework for such observables as a major unresolved challenge. The present work addresses one part of this challenge by deriving analytic expressions for local polarizability changes, but it does not provide a complete theory connecting the spin-glass solution to chemical measurements.

References

Still there are many open questions left and we are at a very early stage to connect the spin glass theory to experiments. One of the major difficulty is the calculation of chemical observables, since the spin glass solution is infinitely degenerate (thermodynamic limit) and thus requires a fundamental non-perturbative discussion of chemical observables.

— Evidence for cavity-induced metallic phase from entropic electron correlation effects  (2608.16593 - Horak et al., 17 Aug 2026) in Introduction, paragraph beginning “Recent theoretical advances show that an energetic collective picture is incomplete”

Coupling this short-range quantum spin-glass sector to itinerant fermions would also provide a setting in which to ask whether different levels of the Parisi hierarchy produce distinct channels of singular fermion scattering and, collectively, non-Fermi-liquid metallic behavior.

— Short-Range Vector Spin Glasses: Parisi Hierarchies and Real-Space Ultrametricity  (2610.12441 - Vijay et al., 8 Oct 2026) in Conclusion and outlook, subsection “Quantum Spin Glasses”