Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor
While the notion of quantum chaos is tied to random matrix spectral correlations, also eigenstate properties in chaotic systems are often assumed to be described by random matrix theory. Analytic insights into eigenstate correlations can be obtained by the recently introduced partial spectral form f...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-04-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-04-17-1709/pdf/ |
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| author | Felix Fritzsch Maximilian F. I. Kieler Arnd Bäcker |
| author_facet | Felix Fritzsch Maximilian F. I. Kieler Arnd Bäcker |
| author_sort | Felix Fritzsch |
| collection | DOAJ |
| description | While the notion of quantum chaos is tied to random matrix spectral correlations, also eigenstate properties in chaotic systems are often assumed to be described by random matrix theory. Analytic insights into eigenstate correlations can be obtained by the recently introduced partial spectral form factor. Here, we study the partial spectral form factor in chaotic dual-unitary quantum circuits in the thermodynamic limit. We compute the latter for a finite subsystem in a brickwork circuit coupled to an infinite complement. For initial times, shorter than the subsystem's size, spatial locality and (dual) unitarity implies a constant partial spectral form factor, clearly deviating from the linear ramp of the random matrix prediction. In contrast, for larger times we prove, that the partial spectral form factor follows the random matrix result up to exponentially suppressed corrections. We supplement our exact analytical results by semi-analytic computations performed in the thermodynamic limit as well as with numerics for finite-size systems. |
| format | Article |
| id | doaj-art-eac5113cb3af49ccb272c98eb0ed6615 |
| institution | DOAJ |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-eac5113cb3af49ccb272c98eb0ed66152025-08-20T03:18:52ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-04-019170910.22331/q-2025-04-17-170910.22331/q-2025-04-17-1709Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form FactorFelix FritzschMaximilian F. I. KielerArnd BäckerWhile the notion of quantum chaos is tied to random matrix spectral correlations, also eigenstate properties in chaotic systems are often assumed to be described by random matrix theory. Analytic insights into eigenstate correlations can be obtained by the recently introduced partial spectral form factor. Here, we study the partial spectral form factor in chaotic dual-unitary quantum circuits in the thermodynamic limit. We compute the latter for a finite subsystem in a brickwork circuit coupled to an infinite complement. For initial times, shorter than the subsystem's size, spatial locality and (dual) unitarity implies a constant partial spectral form factor, clearly deviating from the linear ramp of the random matrix prediction. In contrast, for larger times we prove, that the partial spectral form factor follows the random matrix result up to exponentially suppressed corrections. We supplement our exact analytical results by semi-analytic computations performed in the thermodynamic limit as well as with numerics for finite-size systems.https://quantum-journal.org/papers/q-2025-04-17-1709/pdf/ |
| spellingShingle | Felix Fritzsch Maximilian F. I. Kieler Arnd Bäcker Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor Quantum |
| title | Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor |
| title_full | Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor |
| title_fullStr | Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor |
| title_full_unstemmed | Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor |
| title_short | Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor |
| title_sort | eigenstate correlations in dual unitary quantum circuits partial spectral form factor |
| url | https://quantum-journal.org/papers/q-2025-04-17-1709/pdf/ |
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