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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&apos;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.<\/jats:p>","DOI":"10.22331\/q-2025-04-17-1709","type":"journal-article","created":{"date-parts":[[2025,4,17]],"date-time":"2025-04-17T15:58:01Z","timestamp":1744905481000},"page":"1709","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":5,"title":["Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor"],"prefix":"10.22331","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7659-7574","authenticated-orcid":false,"given":"Felix","family":"Fritzsch","sequence":"first","affiliation":[{"name":"Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1092-5539","authenticated-orcid":false,"given":"Maximilian F. I.","family":"Kieler","sequence":"additional","affiliation":[{"name":"Technische Universit\u00e4t Dresden, Institut f\u00fcr Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4321-8099","authenticated-orcid":false,"given":"Arnd","family":"B\u00e4cker","sequence":"additional","affiliation":[{"name":"Technische Universit\u00e4t Dresden, Institut f\u00fcr Theoretische Physik and Center for Dynamics, 01062 Dresden, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2025,4,17]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"F. J. Dyson. ``The threefold way. Algebraic structure of symmetry groups and ensembles in quantum mechanics''. J. Math. Phys. 3, 1199\u20131215 (1962).","DOI":"10.1063\/1.1703863"},{"key":"1","doi-asserted-by":"publisher","unstructured":"E. Wigner. ``Random matrices in physics''. SIAM Rev. 9, 1\u201323 (1967).","DOI":"10.1137\/1009001"},{"key":"2","unstructured":"M. L. Mehta. ``Random matrices''. Elsevier. San Diego, CA (2004). 3rd edition."},{"key":"3","doi-asserted-by":"publisher","unstructured":"F. Haake. ``Quantum signatures of chaos''. Springer-Verlag. Berlin (2010). 3rd revised and enlarged edition.","DOI":"10.1007\/978-3-642-05428-0"},{"key":"4","doi-asserted-by":"publisher","unstructured":"H.-J. St\u00f6ckmann. ``Quantum chaos: An Introduction''. Cambrige University Press, Cambridge. (2000).","DOI":"10.1017\/CBO9780511524622"},{"key":"5","doi-asserted-by":"publisher","unstructured":"G. Casati, F. Valz-Gris, and I. Guarnieri. ``On the connection between quantization of nonintegrable systems and statistical theory of spectra''. Lett. Nucovo Cimento 28, 279\u2013282 (1980).","DOI":"10.1007\/BF02798790"},{"key":"6","doi-asserted-by":"publisher","unstructured":"M. V. Berry. ``Quantizing a classically ergodic system: Sinai's billiard and the KKR method''. Ann. of Phys. 131, 163\u2013216 (1981).","DOI":"10.1016\/0003-4916(81)90189-5"},{"key":"7","doi-asserted-by":"publisher","unstructured":"O. Bohigas, M. J. Giannoni, and C. Schmit. ``Characterization of chaotic quantum spectra and universality of level fluctuation laws''. Phys. Rev. Lett. 52, 1\u20134 (1984).","DOI":"10.1103\/PhysRevLett.52.1"},{"key":"8","doi-asserted-by":"publisher","unstructured":"M. C. Gutzwiller. ``Chaos in classical and quantum mechanics''. Springer-Verlag, New York. (1990).","DOI":"10.1007\/978-1-4612-0983-6"},{"key":"9","doi-asserted-by":"publisher","unstructured":"M. Sieber and K. Richter. ``Correlations between periodic orbits and their r\u00f4le in spectral statistics''. Phys. Scripta 2001, 128\u2013133 (2001).","DOI":"10.1238\/Physica.Topical.090a00128"},{"key":"10","doi-asserted-by":"publisher","unstructured":"M. Sieber. ``Leading off-diagonal approximation for the spectral form factor for uniformly hyperbolic systems''. J. Phys. A 35, L613\u2013L619 (2002).","DOI":"10.1088\/0305-4470\/35\/42\/104"},{"key":"11","doi-asserted-by":"publisher","unstructured":"S. M\u00fcller, S. Heusler, P. Braun, F. Haake, and A. Altland. ``Semiclassical foundation of universality in quantum chaos''. Phys. Rev. Lett. 93, 014103 (2004).","DOI":"10.1103\/PhysRevLett.93.014103"},{"key":"12","doi-asserted-by":"publisher","unstructured":"L. D'Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol. ``From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics''. Adv. Phys. 65, 239\u2013362 (2016).","DOI":"10.1080\/00018732.2016.1198134"},{"key":"13","doi-asserted-by":"publisher","unstructured":"P. Kos, M. Ljubotina, and T. Prosen. ``Many-body quantum chaos: Analytic connection to random matrix theory''. Phys. Rev. X 8, 021062 (2018).","DOI":"10.1103\/PhysRevX.8.021062"},{"key":"14","doi-asserted-by":"publisher","unstructured":"B. Bertini, P. Kos, and T. Prosen. ``Exact spectral form factor in a minimal model of many-body quantum chaos''. Phys. Rev. Lett. 121, 264101 (2018).","DOI":"10.1103\/PhysRevLett.121.264101"},{"key":"15","doi-asserted-by":"publisher","unstructured":"B. Bertini, P. Kos, and T. Prosen. ``Random matrix spectral form factor of dual-unitary quantum circuits''. Commun. Math. Phys. 387, 597\u2013620 (2021).","DOI":"10.1007\/s00220-021-04139-2"},{"key":"16","doi-asserted-by":"publisher","unstructured":"B. Bertini, P. Kos, and T. Prosen. ``Exact spectral statistics in strongly localized circuits''. Phys. Rev. B 105, 165142 (2022).","DOI":"10.1103\/PhysRevB.105.165142"},{"key":"17","doi-asserted-by":"publisher","unstructured":"A. Chan, A. De Luca, and J. T. Chalker. ``Solution of a minimal model for many-body quantum chaos''. Phys. Rev. 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McClarty, and I. M. Khaymovich. ``Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles''. Phys. Rev. E 105, 014109 (2022).","DOI":"10.1103\/PhysRevE.105.014109"},{"key":"26","doi-asserted-by":"publisher","unstructured":"T. Herrmann, R. Brandau, and A. B\u00e4cker. ``Deviations from random matrix entanglement statistics for kicked quantum chaotic spin-$1\/2$ chains'' (2024). arXiv:2405.07545.","DOI":"10.48550\/arXiv.2405.07545"},{"key":"27","doi-asserted-by":"publisher","unstructured":"A. B\u00e4cker, M.+Haque, and I. M. Khaymovich. ``Multifractal dimensions for random matrices, chaotic quantum maps, and many-body systems''. Phys. Rev. E 100, 032117 (2019).","DOI":"10.1103\/PhysRevE.100.032117"},{"key":"28","doi-asserted-by":"publisher","unstructured":"L. Pausch, E. G. Carnio, A. Rodr\u00edguez, and A. Buchleitner. ``Chaos and ergodicity across the energy spectrum of interacting bosons''. Phys. Rev. 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W. Claeys and A. Lamacraft. ``Maximum velocity quantum circuits''. Phys. Rev. Res. 2, 033032 (2020).","DOI":"10.1103\/PhysRevResearch.2.033032"},{"key":"44","doi-asserted-by":"publisher","unstructured":"B. Gutkin, P. Braun, M. Akila, D. Waltner, and T. Guhr. ``Exact Local Correlations in Kicked Chains''. Phys. Rev. B 102, 174307 (2020).","DOI":"10.1103\/PhysRevB.102.174307"},{"key":"45","doi-asserted-by":"publisher","unstructured":"L. Piroli, B. Bertini, J. I. Cirac, and T. Prosen. ``Exact dynamics in dual-unitary quantum circuits''. Phys. Rev. B 101, 094304 (2020).","DOI":"10.1103\/PhysRevB.101.094304"},{"key":"46","doi-asserted-by":"publisher","unstructured":"B. Bertini and L. Piroli. ``Scrambling in random unitary circuits: Exact results''. Phys. Rev. B 102, 064305 (2020).","DOI":"10.1103\/PhysRevB.102.064305"},{"key":"47","doi-asserted-by":"publisher","unstructured":"Y. Kasim and T. Prosen. ``Dual unitary circuits in random geometries''. J. Phys. A 56, 025003 (2023).","DOI":"10.1088\/1751-8121\/acb1e0"},{"key":"48","doi-asserted-by":"publisher","unstructured":"F. Fritzsch and T. Prosen. ``Boundary chaos''. Phys. Rev. E 106, 014210 (2022).","DOI":"10.1103\/PhysRevE.106.014210"},{"key":"49","doi-asserted-by":"publisher","unstructured":"F. Fritzsch, R. Ghosh, and T. Prosen. ``Boundary chaos: Exact entanglement dynamics''. SciPost Phys. 15, 092 (2023).","DOI":"10.21468\/SciPostPhys.15.3.092"},{"key":"50","doi-asserted-by":"publisher","unstructured":"B. Bertini, P. Kos, and T. Prosen. ``Entanglement spreading in a minimal model of maximal many-body quantum chaos''. Phys. Rev. X 9, 021033 (2019).","DOI":"10.1103\/PhysRevX.9.021033"},{"key":"51","doi-asserted-by":"publisher","unstructured":"M. A. Rampp and P. W. Claeys. ``Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics'' (2023). arXiv:2312.03838.","DOI":"10.48550\/arXiv.2312.03838"},{"key":"52","doi-asserted-by":"publisher","unstructured":"T. Zhou and A. Nahum. ``Entanglement membrane in chaotic many-body systems''. Phys. Rev. X 10, 031066 (2020).","DOI":"10.1103\/PhysRevX.10.031066"},{"key":"53","doi-asserted-by":"publisher","unstructured":"M. A. Rampp, S. A. Rather, and P. W. Claeys. ``The entanglement membrane in exactly solvable lattice models'' (2023). arXiv:2312.12509.","DOI":"10.48550\/arXiv.2312.12509"},{"key":"54","doi-asserted-by":"publisher","unstructured":"B. Bertini, P. Kos, and T. Prosen. ``Operator entanglement in local quantum circuits I: Chaotic dual-unitary circuits''. SciPost Phys. 8, 067 (2020).","DOI":"10.21468\/SciPostPhys.8.4.067"},{"key":"55","doi-asserted-by":"publisher","unstructured":"B. Bertini, P. Kos, and T. Prosen. ``Operator entanglement in local quantum circuits II: Solitons in chains of qubits''. SciPost Phys. 8, 068 (2020).","DOI":"10.21468\/SciPostPhys.8.4.068"},{"key":"56","doi-asserted-by":"publisher","unstructured":"I. Reid and B. Bertini. ``Entanglement barriers in dual-unitary circuits''. Phys. Rev. B 104, 014301 (2021).","DOI":"10.1103\/PhysRevB.104.014301"},{"key":"57","doi-asserted-by":"publisher","unstructured":"P. W. Claeys, M. Henry, J. Vicary, and A. Lamacraft. ``Exact dynamics in dual-unitary quantum circuits with projective measurements''. Phys. Rev. Res. 4, 043212 (2022).","DOI":"10.1103\/PhysRevResearch.4.043212"},{"key":"58","doi-asserted-by":"publisher","unstructured":"J. Yao and P. W. Claeys. ``Temporal entanglement profiles in dual-unitary clifford circuits with measurements'' (2024). arXiv:2404.14374.","DOI":"10.48550\/arXiv.2404.14374"},{"key":"59","doi-asserted-by":"publisher","unstructured":"F. Fritzsch and T. Prosen. ``Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions''. Phys. Rev. E 103, 062133 (2021).","DOI":"10.1103\/PhysRevE.103.062133"},{"key":"60","doi-asserted-by":"publisher","unstructured":"L. Logari\u0107, S. Dooley, S. Pappalardi, and J. Goold. ``Quantum many-body scars in dual-unitary circuits''. Phys. Rev. Lett. 132, 010401 (2024).","DOI":"10.1103\/PhysRevLett.132.010401"},{"key":"61","doi-asserted-by":"publisher","unstructured":"T. Holden-Dye, L. Masanes, and A. Pal. ``Fundamental charges for dual-unitary circuits'' (2023). arXiv:2312.14148.","DOI":"10.48550\/arXiv.2312.14148"},{"key":"62","doi-asserted-by":"publisher","unstructured":"W. W. Ho and S. Choi. ``Exact emergent quantum state designs from quantum chaotic dynamics''. Phys. Rev. Lett. 128, 060601 (2022).","DOI":"10.1103\/PhysRevLett.128.060601"},{"key":"63","doi-asserted-by":"publisher","unstructured":"P. W. Claeys and A. Lamacraft. ``Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics''. Quantum 6, 738 (2022).","DOI":"10.22331\/q-2022-06-15-738"},{"key":"64","doi-asserted-by":"publisher","unstructured":"R. Suzuki, K. Mitarai, and K. Fujii. ``Computational power of one- and two-dimensional dual-unitary quantum circuits''. Quantum 6, 631 (2022).","DOI":"10.22331\/q-2022-01-24-631"},{"key":"65","doi-asserted-by":"publisher","unstructured":"L. Masanes. ``Discrete holography in dual-unitary circuits'' (2023). arXiv:2301.02825.","DOI":"10.48550\/arXiv.2301.02825"},{"key":"66","doi-asserted-by":"publisher","unstructured":"S. Carignano and L. Tagliacozzo. ``Loschmidt echo, emerging dual unitarity and scaling of generalized temporal entropies after quenches to the critical point'' (2024). arXiv:2405.14706.","DOI":"10.48550\/arXiv.2405.14706"},{"key":"67","doi-asserted-by":"publisher","unstructured":"X. Mi et al. ``Information scrambling in quantum circuits''. Science 374, 1479\u20131483 (2021).","DOI":"10.1126\/science.abg5029"},{"key":"68","doi-asserted-by":"publisher","unstructured":"E. Chertkov et al. ``Holographic dynamics simulations with a trapped-ion quantum computer''. Nat. Phys. 18, 1074\u20131079 (2022).","DOI":"10.1038\/s41567-022-01689-7"},{"key":"69","doi-asserted-by":"publisher","unstructured":"R. E. Prange. ``The spectral form factor is not self-averaging''. Phys. Rev. Lett. 78, 2280\u20132283 (1997).","DOI":"10.1103\/PhysRevLett.78.2280"},{"key":"70","doi-asserted-by":"publisher","unstructured":"M. C. Ba\u00f1uls, M. B. Hastings, F. Verstraete, and J. I. Cirac. ``Matrix product states for dynamical simulation of infinite chains''. Phys. Rev. Lett. 102, 240603 (2009).","DOI":"10.1103\/PhysRevLett.102.240603"},{"key":"71","doi-asserted-by":"publisher","unstructured":"P. W. Claeys, A. Lamacraft, and J. Vicary. ``From dual-unitary to biunitary: A 2-categorical model for exactly-solvable many-body quantum dynamics'' (2023). arXiv:2302.07280.","DOI":"10.48550\/arXiv.2302.07280"},{"key":"72","doi-asserted-by":"publisher","unstructured":"S. A. Rather, S. Aravinda, and A. Lakshminarayan. ``Creating ensembles of dual unitary and maximally entangling quantum evolutions''. Phys. Rev. Lett. 125, 070501 (2020).","DOI":"10.1103\/PhysRevLett.125.070501"},{"key":"73","doi-asserted-by":"publisher","unstructured":"S. Aravinda, S. A. Rather, and A. Lakshminarayan. ``From dual-unitary to quantum bernoulli circuits: Role of the entangling power in constructing a quantum ergodic hierarchy''. Phys. Rev. Res. 3, 043034 (2021).","DOI":"10.1103\/PhysRevResearch.3.043034"},{"key":"74","doi-asserted-by":"publisher","unstructured":"T. Prosen. ``Many-body quantum chaos and dual-unitarity round-a-face''. Chaos 31, 093101 (2021).","DOI":"10.1063\/5.0056970"},{"key":"75","doi-asserted-by":"publisher","unstructured":"C. Jonay, V. Khemani, and M. Ippoliti. ``Triunitary quantum circuits''. Phys. Rev. Res. 3, 043046 (2021).","DOI":"10.1103\/PhysRevResearch.3.043046"},{"key":"76","doi-asserted-by":"publisher","unstructured":"T. Gombor and B. 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