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Probing quantum chaos through singular-value correlations in sparse non-Hermitian SYK model

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arxiv 2406.11969 v3 pith:OQAJCY5Q submitted 2024-06-17 quant-ph cond-mat.dis-nncond-mat.str-elhep-th

Pratik Nandy , Tanay Pathak , Masaki Tezuka This is my paper · ORCID
classification quant-phcond-mat.dis-nncond-mat.str-elhep-th
keywords singularnon-hermitianmodelsystemsvaluesanalogouscomplexityfactor
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Utilizing singular value decomposition, our investigation focuses on the spectrum of the singular values within a sparse non-Hermitian Sachdev-Ye-Kitaev (SYK) model. Unlike the complex eigenvalues typical of non-Hermitian systems, singular values are inherently real and positive. Our findings reveal a congruence between the statistics of singular values and those of the analogous Hermitian Gaussian ensembles. An increase in sparsity results in the non-Hermitian SYK model deviating from its chaotic behavior, a phenomenon precisely captured by the singular value ratios. Our analysis of the singular form factor ({\upsigma}FF), analogous to the spectral form factor (SFF) indicates the disappearance of the linear ramp with increased sparsity. Additionally, we define singular complexity, inspired by the spectral complexity in Hermitian systems, whose saturation provides a critical threshold of sparseness. Such disintegration is likely associated with the breakdown of the existing holographic dual for non-Hermitian systems.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Analytic Spread Complexity from Level Statistics: From Chaos to Integrability

    hep-th 2026-08 conditional novelty 7.0 of 10

    The finite-time peak of spread complexity is controlled by the Fourier transform of the nearest-neighbour energy-level spacing distribution.

  2. Krylov-Space Memory Cores

    hep-th 2026-07 conditional novelty 6.0 of 10

    Anomalous initial states in otherwise thermalizing models leave compact, stationary low-depth Krylov-space cores—regions with persistent fluctuations, Gibbs mismatch, and current activity—while generic states do not.

  3. Entanglement production in the Sachdev-Ye-Kitaev Model and its variants

    quant-ph 2025-07 conditional novelty 6.0 of 10

    Entanglement production rates distinguish the spin-SYK model from fermionic SYK and binary SYK, and the differences only become visible at larger system sizes.

  4. Spread Complexity in Non-Hermitian Many-Body Localization Transition

    cond-mat.dis-nn 2024-11 conditional novelty 6.0 of 10

    Singular value spread complexity and TFD-state spread complexity give new numerical order parameters for the non-Hermitian many-body localization transition.

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