Effective non-revelation and Scrooge ensembles in interacting integrable models

Investigate whether effective non-revelation of conserved charges in interacting integrable models leads to a Scrooge ensemble determined by the reduced generalized Gibbs ensemble, or whether additional signatures of integrability persist in higher moments of the projected ensemble.

Background

The paper establishes numerical evidence for a fermionic Gaussian Scrooge ensemble in the non-interacting XX chain at finite temperature. This ensemble is defined directly on the subsystem as a distortion of the Haar measure over pure Gaussian states, chosen so that its first moment equals the reduced generalized Gibbs ensemble.

The authors identify extension to interacting integrable systems as a distinct unresolved direction. Such systems possess interacting quasiparticles and extensive conservation laws beyond the quadratic structure used throughout the paper, so it is unknown whether the same effective washing-out of charge information produces a reduced-GGE-determined Scrooge ensemble or leaves detectable integrability-dependent correlations in higher projected-ensemble moments.

References

Several questions remain open. A natural direction is to extend our analysis to interacting integrable models and investigate whether effective non-revelation leads to a Scrooge ensemble determined by the reduced GGE, or whether additional signatures of integrability persist in the higher moments of the projected ensemble.

— Gaussian Scrooge Ensemble from Deep Thermalization in Free-Fermions  (2610.10279 - Russotto et al., 7 Oct 2026) in Section 6, Conclusions