Haar averaged moments of correlation functions and OTOCs in Floquet systems

TL;DR

This paper derives exact large-q limits for correlation functions and OTOCs in Floquet systems, revealing a principle that simplifies their calculation and enhances understanding of scrambling and thermalisation.

Contribution

It introduces a general method to decompose OTOCs into manageable parts, applicable to Floquet systems, advancing theoretical tools for studying quantum chaos.

Findings

Exact large-q expressions for correlation functions and OTOCs

A general principle for decomposing OTOCs into simpler components

Potential applicability of the method to broader quantum systems

Abstract

Scrambling and thermalisation are topics of intense study in both condensed matter and high energy physics. Random unitary dynamics form a simple testing-ground for our theoretical understanding of these processes. In this work, we derive exact expressions for the large $q$ limiting behaviour of a selection of $n$-point correlation functions, out-of-time-ordered correlators (OTOCs), and their moments. In the process we find a general principle that breaks OTOCs into small and easy to calculate pieces, and which can likely be deployed in a more general context.