2022
DOI: 10.1103/physrevx.12.021040
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Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model

Abstract: Spectral rigidity in Hermitian quantum chaotic systems signals the presence of dynamical universal features at time scales that can be much shorter than the Heisenberg time. We study the analogue of this time scale in many-body non-Hermitian quantum chaos by a detailed analysis of long-range spectral correlators. For that purpose, we investigate the number variance and the spectral form factor of a non-Hermitian q-body Sachdev-Ye-Kitaev (nHSYK) model, which describes N fermions in zero spatial dimensions. Afte… Show more

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Cited by 55 publications
(17 citation statements)
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“…Finding the fingerprint of chaos in such open quantum systems has also become an emerging area of research. The dissipative dynamics are described by non-unitary evolution, for which the RMT has been extended to non-Hermitian complex matrices [376][377][378]. There are attempts to capture the departure from integrability in these open quantum systems from the spectral properties of the non-Hermitian matrices [379].…”
Section: Discussion and Outlookmentioning
confidence: 99%
“…Finding the fingerprint of chaos in such open quantum systems has also become an emerging area of research. The dissipative dynamics are described by non-unitary evolution, for which the RMT has been extended to non-Hermitian complex matrices [376][377][378]. There are attempts to capture the departure from integrability in these open quantum systems from the spectral properties of the non-Hermitian matrices [379].…”
Section: Discussion and Outlookmentioning
confidence: 99%
“…to its relation to Euclidean wormholes [36,61], replica symmetry breaking [47,62], and a symmetry classification [63]. However, these studies have not investigated the mentioned intriguing relation between wormholes in Euclidean time and strongly interacting dissipative systems in real time.…”
Section: Discussionmentioning
confidence: 99%
“…Recently, exact expressions of CSR for the Ginibre unitary ensembles (GinUE) in the large N limit has also been deduced [77]. Since its formulation, the complex spacing ratios have found applications in a wide variety of quantum systems [75][76][77].…”
Section: Complex Spacing Ratiosmentioning
confidence: 99%