Transition to chaos in extended systems and their quantum impurity models

TL;DR

This paper investigates the transition to chaos in extended quantum many-body systems, specifically a chain of Tavis-Cummings models, and introduces a minimal impurity model to replicate spectral properties.

Contribution

It demonstrates how chaos emerges in extended quantum systems and proposes a simplified impurity model to effectively capture their spectral features.

Findings

Transition from integrability to chaos as hopping increases

Spectral properties accurately reproduced by impurity model

Method applicable to other large local Hilbert space lattice models

Abstract

Chaos sets a fundamental limit to quantum-information processing schemes. We study the onset of chaos in spatially extended quantum many-body systems that are relevant to quantum optical devices. We consider an extended version of the Tavis-Cummings model on a finite chain. By studying level-spacing statistics, adjacent gap ratios, and spectral form factors, we observe the transition from integrability to chaos as the hopping between the Tavis-Cummings sites is increased above a finite value. The results are obtained by means of exact numerical diagonalization which becomes notoriously hard for extended lattice geometries. In an attempt to circumvent these difficulties, we identify a minimal single-site quantum impurity model that successfully captures the spectral properties of the lattice model. This approach is intended to be adaptable to other lattice models with large local Hilbert spaces.