Free Cumulants and Full Eigenstate Thermalization from Boundary Scrambling
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916943439593472 |
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| author | Fritzsch, Felix Alves, Gabriel O. Rampp, Michael A. Claeys, Pieter W. |
| author_facet | Fritzsch, Felix Alves, Gabriel O. Rampp, Michael A. Claeys, Pieter W. |
| contents | Out-of-time-order correlation functions (OTOCs) and their higher-order generalizations present important probes of quantum information dynamics and scrambling. We introduce a solvable many-body quantum model, which we term boundary scrambling, for which the full dynamics of higher-order OTOCs is analytically tractable. These dynamics support a decomposition into free cumulants and unify recent extensions of the eigenstate thermalization hypothesis with predictions from random quantum circuit models. We obtain exact expressions for (higher-order) correlations between matrix elements and show these to be stable away from the solvable point. The solvability is enabled by the identification of a higher-order Markovian influence matrix, capturing the effect of the full system on a local subsystem. These results provide insight into the emergence of random-matrix behavior from structured Floquet dynamics and show how techniques from free probability can be applied in the construction of exactly-solvable many-body models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08060 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Free Cumulants and Full Eigenstate Thermalization from Boundary Scrambling Fritzsch, Felix Alves, Gabriel O. Rampp, Michael A. Claeys, Pieter W. Quantum Physics Statistical Mechanics Mathematical Physics Chaotic Dynamics Exactly Solvable and Integrable Systems Out-of-time-order correlation functions (OTOCs) and their higher-order generalizations present important probes of quantum information dynamics and scrambling. We introduce a solvable many-body quantum model, which we term boundary scrambling, for which the full dynamics of higher-order OTOCs is analytically tractable. These dynamics support a decomposition into free cumulants and unify recent extensions of the eigenstate thermalization hypothesis with predictions from random quantum circuit models. We obtain exact expressions for (higher-order) correlations between matrix elements and show these to be stable away from the solvable point. The solvability is enabled by the identification of a higher-order Markovian influence matrix, capturing the effect of the full system on a local subsystem. These results provide insight into the emergence of random-matrix behavior from structured Floquet dynamics and show how techniques from free probability can be applied in the construction of exactly-solvable many-body models. |
| title | Free Cumulants and Full Eigenstate Thermalization from Boundary Scrambling |
| topic | Quantum Physics Statistical Mechanics Mathematical Physics Chaotic Dynamics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2509.08060 |