Structural Stability Hypothesis of Dual Unitary Quantum Chaos
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912007772438528 |
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| author | Riddell, Jonathon von Keyserlingk, Curt Prosen, Tomaž Bertini, Bruno |
| author_facet | Riddell, Jonathon von Keyserlingk, Curt Prosen, Tomaž Bertini, Bruno |
| contents | Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any semiclassical limit. Although this property is extremely difficult to prove analytically for generic many-body systems, a rigorous proof has been achieved for dual-unitary circuits -- a special class of local quantum circuits that remain unitary upon swapping space and time. Here we consider the fate of this property when moving from dual-unitary to generic quantum circuits focussing on the \emph{spectral form factor}, i.e., the Fourier transform of the two-point correlation. We begin with a numerical survey that, in agreement with previous studies, suggests that there exists a finite region in parameter space where dual-unitary physics is stable and spectral correlations are still described by random matrix theory, although up to a maximal quasienergy scale. To explain these findings, we develop a perturbative expansion: it recovers the random matrix theory predictions, provided the terms occurring in perturbation theory obey a relatively simple set of assumptions. We then provide numerical evidence and a heuristic analytical argument supporting these assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_19096 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Structural Stability Hypothesis of Dual Unitary Quantum Chaos Riddell, Jonathon von Keyserlingk, Curt Prosen, Tomaž Bertini, Bruno Statistical Mechanics High Energy Physics - Theory Mathematical Physics Chaotic Dynamics Quantum Physics Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any semiclassical limit. Although this property is extremely difficult to prove analytically for generic many-body systems, a rigorous proof has been achieved for dual-unitary circuits -- a special class of local quantum circuits that remain unitary upon swapping space and time. Here we consider the fate of this property when moving from dual-unitary to generic quantum circuits focussing on the \emph{spectral form factor}, i.e., the Fourier transform of the two-point correlation. We begin with a numerical survey that, in agreement with previous studies, suggests that there exists a finite region in parameter space where dual-unitary physics is stable and spectral correlations are still described by random matrix theory, although up to a maximal quasienergy scale. To explain these findings, we develop a perturbative expansion: it recovers the random matrix theory predictions, provided the terms occurring in perturbation theory obey a relatively simple set of assumptions. We then provide numerical evidence and a heuristic analytical argument supporting these assumptions. |
| title | Structural Stability Hypothesis of Dual Unitary Quantum Chaos |
| topic | Statistical Mechanics High Energy Physics - Theory Mathematical Physics Chaotic Dynamics Quantum Physics |
| url | https://arxiv.org/abs/2402.19096 |