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This preprint offers a pedagogical overview of eigenstate thermalization, explaining how isolated quantum systems reach thermal equilibrium under unitary dynamics. The authors leverage random matrix theory and volume-law entanglement entropy to contextualize these behaviors within quantum many-body systems. For researchers in quantum chaos and statistical mechanics, this work serves as a foundational resource connecting theoretical frameworks with numerical evidence.
Eigenstate thermalization
arXiv:2604.11872v3 Announce Type: replace Abstract: We provide a pedagogical introduction to eigenstate thermalization. This phenomenon, which occurs in generic quantum systems, allows one to understand why thermalization takes place in isolated systems under unitary dynamics. We motivate eigenstate thermalization using random matrix theory and discuss recent complementary results for the volume-law entanglement entropy of Haar-random states. We discuss numerical results that highlight the corresponding behaviors in quantum many-body systems.
Abstract:We provide a pedagogical introduction to eigenstate thermalization. This phenomenon, which occurs in generic quantum systems, allows one to understand why thermalization takes place in isolated systems under unitary dynamics. We motivate eigenstate thermalization using random matrix theory and discuss recent complementary results for the volume-law entanglement entropy of Haar-random states. We discuss numerical results that highlight the corresponding behaviors in quantum many-body systems.
23 pages, 9 figures; Chapter for the Quantum Chaos volume in 'Comprehensive Quantum Mechanics', to be published by Elsevier (Main editor: R.B. Mann; volume editors: S. Gnutzmann and K. Życzkowski)
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)
arXiv:2604.11872 [quant-ph]
(or arXiv:2604.11872v3 [quant-ph] for this version)
Full text under the publisher's open licence · 108 words
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