Scramblon loops

TL;DR

This paper investigates the self-interactions of the scramblon in large N chaotic quantum systems, revealing how loop fluctuations affect the single-scramblon approximation differently in high and low temperature regimes.

Contribution

It analyzes the impact of scramblon self-interactions in extended SYK models, highlighting the breakdown of the single-scramblon approximation due to loop effects.

Findings

Loop fluctuations can invalidate the single-scramblon approximation before OTOC contributions become significant.

A qualitative difference exists between high-temperature incoherent and low-temperature coherent regimes.

Self-interactions are more prominent in spatially extended models at large separation.

Abstract

In large $N$ chaotic quantum systems, the butterfly effect is mediated by a collective field mode known as the ``scramblon.'' We study self-interactions of the scramblon in variants of the Sachdev-Ye-Kitaev model. In spatially extended versions of the model and for large spatial separation, fluctuations described by loop diagrams can invalidate the single-scramblon approximation well before its contribution to out-of-time-order correlators becomes of order one. We find a qualitative difference between an incoherent regime at high temperaure (or in a Brownian version of the model) and a coherent regime at low temperature.