Quantum Chaos in Random Ising Networks

TL;DR

This paper investigates quantum chaos signatures in the transverse field Ising model on Erdős-Rényi networks, revealing how spectral measures indicate the transition between chaotic and integrable regimes as network connectivity varies.

Contribution

It provides a systematic analysis of quantum chaos indicators in Ising networks with varying connectivity, highlighting the conditions under which chaos persists or breaks down.

Findings

Spectral measures detect chaos breakdown with changing connectivity.

Level spacing and spectral form factor signal chaos in dense networks.

Velocity statistics reveal chaos signatures in sparse networks.

Abstract

We report a systematic investigation of universal quantum chaotic signatures in the transverse field Ising model on an Erd\H{o}s-R\'enyi network. This is achieved by studying local spectral measures such as the level spacing and the level velocity statistics. A spectral form factor analysis is also performed as a global measure, probing energy level correlations at arbitrary spectral distances. Our findings show that these measures capture the breakdown of chaotic behavior upon varying the connectivity and strength of the transverse field in various regimes. We demonstrate that the level spacing statistics and the spectral form factor signal this breakdown for sparsely and densely connected networks. The velocity statistics capture the surviving chaotic signatures in the sparse limit. However, these integrable-like regimes extend over a vanishingly small segment in the full range of connectivity.