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

Abstract

A bstract In this work, we investigate the quantum chaos in various $$ T\overline{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> -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.