Information Scrambling and Entanglement Dynamics of Complex Brownian Sachdev-Ye-Kitaev Models

TL;DR

This paper investigates how information scrambling and entanglement evolve in complex Brownian Sachdev-Ye-Kitaev models, deriving effective theories and analyzing the effects of charge density and measurements on quantum chaos.

Contribution

It introduces a new effective theory for scramblons in cBSYK models and explores the charge density dependence of entanglement velocity and measurement-induced transitions.

Findings

Derived closed-form expressions for late-time OTOC and operator size.

Established the density dependence of entanglement velocity and its relation to butterfly velocity.

Identified symmetry properties of measurement-induced transitions in non-interacting models.

Abstract

In this work, we study the information scrambling and the entanglement dynamics in the complex Brownian Sachdev-Ye-Kitaev (cBSYK) models, focusing on their dependence on the charge density $n$. We first derive the effective theory for scramblons in a single cBSYK model, which gives closed-form expressions for the late-time OTOC and operator size. In particular, the result for OTOC is consistent with numerical observations in [1]. We then study the entanglement dynamics in cBSYK chains. We derive the density dependence of the entanglement velocity for both R\'enyi entropies and the Von Neumann entropy, with a comparison to the butterfly velocity. We further consider adding repeated measurements and derive the effective theory of the measurement induced transition which shows $U(2)_L\otimes U(2)_R$ symmetry for non-interacting models.