Single-Particle Universality of the Many-Body Spectral Form Factor
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913804962496512 |
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| author | Flynn, Michael O. Vidmar, Lev Ikeda, Tatsuhiko N. |
| author_facet | Flynn, Michael O. Vidmar, Lev Ikeda, Tatsuhiko N. |
| contents | We consider systems of fermions evolved by non-interacting unitary circuits with correlated on-site potentials. When these potentials are drawn from the eigenvalue distribution of a circular random matrix ensemble, the single-particle sector exhibits chaotic dynamics. We study the corresponding many-body spectral statistics and show that the spectral form factor (SFF) can be computed \textit{exactly}. Due to the absence of interactions the SFF grows exponentially in time, a result which we demonstrate through simple arguments, scaling collapses, and closed-form evaluation of the SFF. We study the role of interactions by numerically analyzing a kicked Ising model and find that the SFF crosses over to a linear growth regime consistent with many-body random matrix universality. Our exact results for the SFF provide a baseline for future studies of the crossover between single-particle and many-body random matrix behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07306 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Single-Particle Universality of the Many-Body Spectral Form Factor Flynn, Michael O. Vidmar, Lev Ikeda, Tatsuhiko N. Statistical Mechanics Disordered Systems and Neural Networks Strongly Correlated Electrons Quantum Physics We consider systems of fermions evolved by non-interacting unitary circuits with correlated on-site potentials. When these potentials are drawn from the eigenvalue distribution of a circular random matrix ensemble, the single-particle sector exhibits chaotic dynamics. We study the corresponding many-body spectral statistics and show that the spectral form factor (SFF) can be computed \textit{exactly}. Due to the absence of interactions the SFF grows exponentially in time, a result which we demonstrate through simple arguments, scaling collapses, and closed-form evaluation of the SFF. We study the role of interactions by numerically analyzing a kicked Ising model and find that the SFF crosses over to a linear growth regime consistent with many-body random matrix universality. Our exact results for the SFF provide a baseline for future studies of the crossover between single-particle and many-body random matrix behavior. |
| title | Single-Particle Universality of the Many-Body Spectral Form Factor |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2410.07306 |