Anatomy of information scrambling and decoherence in the integrable Sachdev-Ye-Kitaev model

Abstract

The growth of information scrambling, captured by out-of-time-order correlation functions (OTOCs), is a central indicator of the nature of many-body quantum dynamics. Here, we compute analytically the complete time dependence of the OTOC for an integrable Sachdev-Ye-Kitaev (SYK) model, $N$ Majoranas with random two-body interactions of infinite range, coupled to a Markovian bath at finite temperature. In the limit of no coupling to the bath, the time evolution of scrambling experiences different stages. For $t\lesssim \sqrt{N}$, after an initial polynomial growth, the OTOC approaches saturation in a power-law fashion with oscillations superimposed. At $t\sim \sqrt{N}$, the OTOC reverses trend and starts to decrease linearly in time. The reason for this linear decrease is that, despite being a subleading $1/N$ effect, the OTOC in this region is governed by the spectral form factor of the antisymmetric couplings of the SYK model. The linear decrease stops at $t\sim 2N$, the Heisenberg time, where saturation occurs. The effect of the environment is an overall exponential decay of the OTOC for times longer than the inverse of the coupling strength to the bath. The oscillations at $t\lesssim \sqrt{N}$ indicate lack of thermalization -- a desired feature for a better performance of quantum information devices.

10 pages, 3 figures. v2: added references. v3: as published

References in corpus (13)

• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• A Generalization of Sachdev-Ye-Kitaev
• Chaos, Complexity, and Random Matrices
• Lindbladian dissipation of strongly-correlated quantum matter
• Lindbladian dynamics of the Sachdev-Ye-Kitaev model
• Scrambling Transition in a Radiative Random Unitary Circuit
• Keldysh Wormholes and Anomalous Relaxation in the Dissipative Sachdev-Ye-Kitaev Model
• The quantum regression theorem for out-of-time-ordered correlation functions
• Information Scrambling and Entanglement Dynamics of Complex Brownian Sachdev-Ye-Kitaev Models
• Quantum chaos without false positives
• Robustness of quantum chaos and anomalous relaxation in open quantum circuits
• Quantum Lyapunov exponent in dissipative systems

Cited by in corpus (1)

• From single-particle to many-body chaos in Yukawa--SYK: theory and a cavity-QED proposal