Characterizing the transition from topology to chaos in a kicked quantum system

TL;DR

This paper explores how a quantum top system transitions from topologically protected states to chaotic behavior as the strength of periodic kicks increases, combining theoretical analysis with numerical validation.

Contribution

It provides a detailed theoretical framework and analytic predictions for the transition from topology to chaos in a driven quantum system, supported by numerical evidence.

Findings

Localized topological states proliferate with increasing kicks

Delocalization of states signals onset of chaos

Analytic predictions match numerical level spacing and entropy results

Abstract

This work theoretically investigates the transition from topology to chaos in a periodically driven system consisting of a quantum top coupled to a spin-1/2 particle. The system is driven by two alternating interaction kicks per period. For small kick strengths, localized topologically protected bound states exist, and as the kick strengths increase, these states proliferate. However, at large kick strengths they gradually delocalize in stages, eventually becoming random orthonormal vectors as chaos emerges. We identify the delocalization of the bound states as a finite size effect where their proliferation leads to their eventual overlap. This insight allows us to make analytic predictions for the onset and full emergence of chaos which are supported by numerical results of the quasi-energy level spacing ratio and R\'enyi entropy. A dynamical probe is also proposed to distinguish chaotic from regular behavior.