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

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 our previous work [Mondal, Sinha, and Sinha, Phys. Rev. E 102, 020101(R) (2020)2470-004510.1103/PhysRevE.102.020101]. In this work, we present a detailed analysis of the different type of transitions in the 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 nonergodic 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 nonequilibrium dynamics. Finally, we discuss the detection of nonergodic behavior and different types of quantum scars using "out-of-time-order correlators," which has relevance in the recent experiments.