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.
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BibTeX
@misc{russotto2026gaussian,
title = {{Gaussian Scrooge Ensemble from Deep Thermalization in Free-Fermions}},
author = {Angelo Russotto and Katja Klobas and Pasquale Calabrese and Bruno Bertini},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10279},
eprint = {2610.10279},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10279},
}
RIS
TY - UNPB
TI - Gaussian Scrooge Ensemble from Deep Thermalization in Free-Fermions
AU - Angelo Russotto
AU - Katja Klobas
AU - Pasquale Calabrese
AU - Bruno Bertini
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.10279
UR - https://arxiv.org/abs/2610.10279
AB - 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.
ER -