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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Main Authors: Felix Fritzsch, Maximilian F. I. Kieler, Arnd Bäcker
Format: Article
Language:English
Published: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 2025-04-01
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.
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publisher Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
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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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