Scar Full Eigenstate Thermalization Hypothesis
- URL: http://arxiv.org/abs/2605.26389v1
- Date: Mon, 25 May 2026 23:41:29 GMT
- Title: Scar Full Eigenstate Thermalization Hypothesis
- Abstract summary: The eigenstate thermalization hypothesis (ETH) provides a fundamental mechanism for emergent statistical mechanics in isolated quantum systems.<n>We numerically demonstrate the validity of this framework in the paradigmatic model of quantum scars, the PXP model.
- Score: 3.6521685337900656
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The eigenstate thermalization hypothesis (ETH) provides a fundamental mechanism for emergent statistical mechanics in isolated chaotic quantum systems, asserting that individual energy eigenstates behave as pseudorandom vectors within an energy window. This enables a complete characterization of nontrivial correlations among matrix elements in the energy eigenbasis, as described by the full ETH ansatz. Nevertheless, this description breaks down in systems exhibiting quantum many-body scars, which host non-thermal eigenstates with extensive energy. In this Letter, we address this problem by formulating the \textit{scar full ETH}, which captures correlations among matrix elements involving scar states. The corresponding scaling forms and factorization properties are established using typicality arguments. Multi-time correlation functions for scar states are then organized in terms of both thermal and scar cumulants, providing a nontrivial reorganization of higher-order correlations. We numerically demonstrate the validity of this framework in the paradigmatic model of quantum scars, the PXP model. Our results pave the way for a systematic understanding of intriguing correlations in systems with quantum many-body scars.
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