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Quantum chaos, scrambling and operator growth in $T\bar{T}$ deformed SYK models
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abstract
In this work, we investigate the quantum chaos in various $T\bar{T}$-deformed SYK models with finite $N$, including the SYK$_4$, the supersymmetric SYK$_4$, and the SYK$_2$ models. We numerically study the evolution of the spectral form factor (SFF), the out-of-time ordered correlator (OTOC), and the Krylov complexity. We find that the characteristic evolution of the SFF, OTOC and K-complexity of both the SYK$_4$ and SSYK$_4$ models remains unchanged under the deformation, which implies that the properties of quantum chaos is preserved. We also identify a many-body localization behavior in the deformed SYK$_2$ model.
Forward citations
Cited by 2 Pith papers
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Krylov Complexity of Supersymmetric SYK Models
In finite-size N=2 SYK, breaking supersymmetry with an irrelevant deformation pushes late-time Krylov complexity to roughly half the maximal Krylov-space bound, while a mass deformation leaves saturation complexity a ...
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Butterfly effect and $\textrm{T}\overline{\textrm{T}}$-deformation
For T\bar{T}-deformed BTZ black holes, the butterfly velocity is v_B = sqrt(1 - 8π² μ/β²), exceeding the Mezei-Stanford bound for μ<0 while the Lyapunov exponent stays at the maximal value 2π/β.
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