Quantum criticality and dynamical instability in the kicked top

TL;DR

This paper explores how dynamical instability in the kicked top leads to critical behavior in its quasienergy spectrum, revealing a logarithmic divergence in the density of states and proposing an experimental protocol to observe related magnetization cusp behavior.

Contribution

It analytically demonstrates a logarithmic divergence in the density of states due to dynamical instability and relates it to excited state quantum phase transitions in driven systems.

Findings

Logarithmic divergence in the density of states near critical quasienergy

Analytical connection between dynamical instability and quantum phase transition

Proposed protocol to observe magnetization cusp behavior

Abstract

We investigate precursors of critical behavior in the quasienergy spectrum due to the dynamical instability in the kicked top. Using a semiclassical approach, we analytically obtain a logarithmic divergence in the density of states, which is analogous to a continuous excited state quantum phase transition in undriven systems. We propose a protocol to observe the cusp behavior of the magnetization close to the critical quasienergy.