Gaussian Scrooge Ensemble from Deep Thermalization in Free-Fermions

Abstract:Deep thermalization indicates the emergence of universal ensembles of pure states in a subsystem after measuring its environment. We investigate this phenomenon in a free-fermion chain using local measurements that preserve Gaussianity and break particle-number conservation. Although the measurement outcomes provide partial information about local conserved charges within a finite subsystem, we argue that this information becomes negligible in the thermodynamic limit. This effective non-revelation underlies the emergence of a fermionic Gaussian Scrooge ensemble, determined by the subsystem's generalized Gibbs ensemble. We construct this universal ensemble directly at the subsystem level and provide numerical evidence that it describes the late-time projected ensemble at finite temperature. Our results extend the description of thermalization in non-interacting integrable systems beyond the reduced density matrix to universal statistics of conditional pure states.

Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)

arXiv:2610.10279 [cond-mat.stat-mech]

(or arXiv:2610.10279v1 [cond-mat.stat-mech] for this version)

https://doi.org/10.48550/arXiv.2610.10279 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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