TL;DR
Eigenstate thermalization explains how isolated quantum systems naturally evolve towards thermal equilibrium, supported by random matrix theory and numerical evidence.
Contribution
The paper offers a pedagogical overview of eigenstate thermalization, connecting random matrix theory and numerical results to understand thermalization in quantum systems.
Findings
Eigenstate thermalization accounts for thermalization in isolated quantum systems.
Random matrix theory supports the eigenstate thermalization hypothesis.
Numerical results show volume-law entanglement entropy 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.
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