Non-ergodicity in the Anisotropic Dicke model

TL;DR

This paper investigates the transition between ergodic and non-ergodic phases in a generalized Dicke model, revealing its connection to integrability and suggesting a quantum analogue of the KAM theorem, with implications for quantum phase transitions.

Contribution

It demonstrates that the ergodic--non-ergodic transition is linked to the proximity to integrability in the model, and clarifies its independence from the normal--superradiant phase transition.

Findings

Transition occurs near integrable limit when one coupling is zero

Level statistics and out-of-time correlations reveal the transition

No intrinsic link between ergodic transition and superradiant phase

Abstract

We study the ergodic -- non-ergodic transition in a generalized Dicke model with independent co- and counter rotating light-matter coupling terms. By studying level statistics, the average ratio of consecutive level spacings, and the quantum butterfly effect (out-of-time correlation) as a dynamical probe, we show that the ergodic -- non-ergodic transition in the Dicke model is a consequence of the proximity to the integrable limit of the model when one of the couplings is set to zero. This can be interpreted as a hint for the existence of a quantum analogue of the classical Kolmogorov-Arnold-Moser theorem. Besides, we show that there is no intrinsic relation between the ergodic -- non-ergodic transition and the precursors of the normal -- superradiant quantum phase transition.