Quantum transitions, ergodicity, and quantum scars in the coupled top model

TL;DR

This paper analyzes the coupled top quantum spin model, exploring quantum transitions, ergodicity, and quantum scars, and introduces methods to detect non-ergodic states and quantum scars through out-of-time-order correlators.

Contribution

It provides a detailed analysis of quantum transitions and ergodicity in the coupled top model, linking them to collective spin dynamics and identifying non-ergodic multifractal states.

Findings

Identification of quantum scars and their connection to non-ergodic states.

Quantification of ergodicity using entanglement entropy and multifractal dimensions.

Proposal of out-of-time-order correlators for detecting non-ergodic behavior.

Abstract

We consider an interacting collective spin model known as coupled top (CT), exhibiting a rich variety of phenomena related to quantum transitions, ergodicity, and formation of quantum scars, discussed in [Phys. Rev. E 102, 020101(R) (2020)]. In this work, we present a detailed analysis of the different type of transitions in CT model, and find their connection with the underlying collective spin dynamics. Apart from the quantum scarring phenomena, we also identify another source of deviation from ergodicity due to the presence of non-ergodic multifractal states. The degree of ergodicity of the eigenstates across the energy band is quantified from the relative entanglement entropy as well as multifractal dimensions, which can be probed from non-equilibrium dynamics. Finally, we discuss the detection of non-ergodic behavior and different types of quantum scars using `out-of-time-order correlators', which has relevance in the recent experiments.