Chaos and Scrambling in Quantum Small Worlds

TL;DR

This paper introduces quantum small-world networks by adding long-range interactions to a spin chain and studies their scrambling behavior, revealing increased scrambling with randomness but no signs of chaos.

Contribution

It presents a novel framework for quantum small-worlds and analyzes their scrambling properties using OTOC and SFF, bridging ordered and chaotic quantum regimes.

Findings

Scrambling increases with randomness in interactions

No evidence of quantum chaos in the studied systems

Quantum small-worlds interpolate between order and chaos

Abstract

Quantum small-worlds are quantum many-body systems that interpolate between completely ordered (nearest-neighbour, next-to-nearest-neighbour etc.) and completely random interactions. As such, they furnish a novel new laboratory to study quantum systems transitioning between regular and chaotic behaviour. In this article, we introduce the idea of a quantum small-world network by starting from a well understood integrable system, a spin-1 Heisenberg chain. We then inject a small number of long-range interactions into the spin chain and study its ability to scramble quantum information using two primary devices: the out-of-time-order correlator (OTOC) and the spectral form factor (SFF). We find that the system shows increasingly rapid scrambling as its interactions become progressively more random, with no evidence of quantum chaos.