Unveiling operator growth in SYK quench dynamics

TL;DR

This paper investigates how operator growth and quantum chaos manifest in SYK model quench dynamics by analyzing spin-spin correlation functions, providing a potential experimental probe for chaos in strongly correlated systems.

Contribution

It introduces a method to distinguish operator hopping from operator growth in SYK quench dynamics using correlation functions, linking operator growth to quantum chaos.

Findings

Correlation functions are sensitive to operator locality.

Operator growth can be distinguished from hopping dynamics.

Potential experimental tool for probing quantum chaos.

Abstract

We study non-equilibrium dynamics induced by a sudden quench of strongly correlated Hamiltonians with all-to-all interactions. By relying on a Sachdev-Ye-Kitaev (SYK) based quench protocol, we show that the time evolution of simple spin-spin correlation functions is highly sensitive to the degree of locality of the corresponding operators, once an appropriate set of fundamental fields is identified. By tracking the time-evolution of specific spin-spin correlation functions and their decay, we argue that it is possible to distinguish between operator hopping and operator growth dynamics; the latter being a hallmark of quantum chaos in many-body quantum systems. Such observation, in turn, could constitute a promising tool to probe the emergence of chaotic behavior, rather accessible in state-of-the-art quench setups.