Quantum chaos, scrambling and operator growth in $T\bar{T}$ deformed SYK models

TL;DR

This paper explores how $Tar{T}$ deformation affects quantum chaos in various SYK models, finding preserved chaos in higher models and localization in the SYK$_2$ variant.

Contribution

It provides the first detailed numerical analysis of $Tar{T}$ deformation effects on spectral form factor, OTOC, and Krylov complexity in finite-$N$ SYK models.

Findings

Chaos properties remain unchanged in SYK$_4$ and SSYK$_4$ models under deformation.

Deformed SYK$_2$ exhibits many-body localization behavior.

Spectral form factor, OTOC, and Krylov complexity are used to characterize chaos.

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.