The butterfly effect in a Sachdev-Ye-Kitaev quantum dot system

TL;DR

This paper investigates chaos in a lattice SYK model with quadratic perturbations by analyzing the out-of-time-order correlator, revealing a ballistic front separating chaotic regimes and calculating its velocity across parameters.

Contribution

It introduces the first calculation of front velocity in SYK-like models, extending understanding of chaos propagation in lattice SYK systems with perturbations.

Findings

Identifies a ballistic front separating well-developed and weak chaos regions.

Calculates front velocity for various system parameters.

Validates results across different time scales, including beyond the Ehrenfest time.

Abstract

We study the out-of-time-order correlation function (OTOC) in a lattice extension of the Sachdev-Ye-Kitaev (SYK) model with quadratic perturbations. The results obtained are valid for arbitrary time scales, both shorter and longer than the Ehrenfest time. We demonstrate that the region of well-developed chaos is separated from the weakly chaotic region by the "front region", which moves ballistically across the lattice. Front velocity is calculated for various system's parameters, for the first time for SYK-like models.