# Scrambling of Quantum Information in Quantum Many-Body Systems

## TL;DR

This paper investigates how quantum information spreads in many-body systems, revealing that scrambling is independent of chaos and varies with disorder, using numerical methods and tripartite mutual information as a key measure.

## Contribution

It demonstrates that quantum information scrambling is independent of Hamiltonian integrability and explores its behavior in disordered systems like MBL and SYK models.

## Key findings

- Scrambling can occur in both integrable and non-integrable systems.
- Scrambling is slower in many-body localized phases.
- Disorder in SYK models smooths out scrambling without slowing it.

## Abstract

We systematically investigate scrambling (or delocalizing) processes of quantum information encoded in quantum many-body systems by using numerical exact diagonalization. As a measure of scrambling, we adopt the tripartite mutual information (TMI) that becomes negative when quantum information is delocalized. We clarify that scrambling is an independent property of integrability of Hamiltonians; TMI can be negative or positive for both integrable and non-integrable systems. This implies that scrambling is a separate concept from conventional quantum chaos characterized by non-integrability. Furthermore, we calculate TMI in disordered systems such as many-body localized (MBL) systems and the Sachdev-Ye-Kitaev (SYK) model. We find that scrambling occurs but is slow in a MBL phase, while disorder in the SYK model does not make scrambling slower but makes it smoother.