Entanglement in two-quasiparticle-triaxial-rotor systems: Chirality, wobbling, and the Pauli effect

We investigate the entanglement in two-quasiparticle plus triaxial-rotor (PTR) model for the particle-hole configuration $\pi(1h_{11/2})^1 \otimes \nu(1h_{11/2})^{-1}$, the particle-particle configuration $\pi(1h_{11/2})^1 \otimes \nu(1h_{11/2})^1$, and two-proton particles configuration $\pi(1h_{11/2})^2$ for different values of the triaxiality parameter. The entanglement between the angular momenta of the two quasiparticles and the total angular momentum is quantified by the three bipartite concurrences $\mathcal{C}$ of one type of angular momentum with the other two angular momenta and the area $\mathcal{F}$ of the triangle formed by the bipartite concurrences. Collective chiral and wobbling modes are identified for $\gamma>15^\circ$ via spin coherent state (SCS) maps and spin squeezed state (SSS) plots. Their entanglement increases from moderate values at the band head to near-maximal values at $I=20$. The area $\mathcal{F}$ of the chiral partners changes order as function of $I$ which reflects the crossing of the partner bands as a signature of chirality. For the $\pi(1h_{11/2})^2$ configuration, the antisymmetrization required by the Pauli exclusion principle causes strong entanglement between the two protons, which significantly amplifies the area $\mathcal{F}$. For $\gamma<15^\circ$, the lowest bands become various uniformly rotating quasiparticle configurations, which have large values of $\mathcal{F}$ for all values $I$.