Algebraic description of the triaxially to axially rotational shape phase transition

Within the framework of the interacting boson model, we propose a novel algebraic scheme to describe spin-dependent structural evolutions in triaxial nuclei. Our analysis demonstrates that a triaxially to axially rotational shape phase transition can be induced by the high-order correction which is microscopically motivated by the pairing interaction on the $\gamma$-unstable rotation. This prescription is further applied to describe the structural evolutions along the yrast sequences of $^{132}$Ba and $^{130}$Xe, providing an exemplary case for demonstrating a unified explanation of both low-energy collective structures and high-spin phenomena in O(6)-like nuclei.