Single-eigenstate test of eigenstate thermalization hypothesis via perturbed eigenstate quench

• URL: http://arxiv.org/abs/2608.04696v1
• Date: Wed, 05 Aug 2026 11:06:49 GMT
• Title: Single-eigenstate test of eigenstate thermalization hypothesis via perturbed eigenstate quench
• Abstract summary: We numerically validate an efficient single-eigenstate diagnostic for the eigenstate thermalization hypothesis (ETH) based on a perturbed eigenstate quench protocol.<n>We benchmark the criterion across paradigmatic one-dimensional spin chains covering chaotic, integrable, many-body localized, and quantum many-body scar regimes.
• Score: 0.6138671548064355
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose and numerically validate an efficient single-eigenstate diagnostic for the eigenstate thermalization hypothesis (ETH) based on a perturbed eigenstate quench protocol. By introducing a weak random perturbation to an energy eigenstate to break its stationarity, we characterize the time-averaged subsystem evolution speed as a function of the subsystem-to-total system size ratio. The diagnostic relies on a robust qualitative distinction: eigenstates satisfying ETH exhibit an S-shaped curve with a clear inflection point near half the system size, while ETH-violating eigenstates display a convex J-shaped profile. We benchmark the criterion across paradigmatic one-dimensional spin chains covering chaotic, integrable, many-body localized, and quantum many-body scar regimes, obtaining full agreement with established thermalization phenomenology. Our method circumvents the need for explicit thermal ensemble construction, providing a robust, experimentally feasible probe of eigenstate thermalization at the single-eigenstate level.

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