Absence of operator growth for average equal-time observables in charge-conserved sectors of the Sachdev-Ye-Kitaev model

Year: 2023

Authors: Paviglianiti A., Bandyopadhyay S., Uhrich P., Hauke P.

Autors Affiliation: Univ Trento, Pitaevskii BEC Ctr, INO CNR, Via Sommar 14, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, Via Sommar 14, I-38123 Trento, Italy; Int Sch Adv Studies SISSA, Via Bonomea 265, I-34136 Trieste, Italy; INFN TIFPA, Trento Inst Fundamental Phys & Applicat, Trento, Italy.

Abstract: Quantum scrambling plays an important role in understanding thermalization in closed quantum systems. By this effect, quantum information spreads throughout the system and becomes hidden in the form of non-local correlations. Alternatively, it can be described in terms of the increase in complexity and spatial support of operators in the Heisenberg picture, a phenomenon known as operator growth. In this work, we study the disordered fully-connected Sachdev-Ye-Kitaev (SYK) model, and we demonstrate that scrambling is absent for disorder-averaged expectation values of observables. In detail, we adopt a formalism typical of open quantum systems to show that, on average and within charge-conserved sectors, operators evolve in a relatively simple way which is governed by their operator size. This feature only affects single-time correlation functions, and in particular it does not hold for out-of-time-order correlators, which are well-known to show scrambling behavior. Making use of these findings, we develop a cumulant expansion approach to approximate the evolution of equal-time observables. We employ this scheme to obtain analytic results that apply to arbitrary system size, and we benchmark its effectiveness by exact numerics. Our findings shed light on the structure of the dynamics of observables in the SYK model, and provide an approximate numerical description that overcomes the limitation to small systems of standard methods.

Journal/Review: JOURNAL OF HIGH ENERGY PHYSICS

Volume: (3)      Pages from: 126-1  to: 126-23

KeyWords: Quantum Dissipative Systems; Random Systems; Black Holes
DOI: 10.1007/JHEP03(2023)126

Citations: 2
data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-10-20
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