Eigenstate entanglement in integrable collective spin models

The average entanglement entropy (EE) of the energy eigenstates in non-vanishing partitions has been recently proposed as a diagnostic integrability quantum many-body systems. For it to be faithful characterization integrability, should distinguish systems with well-defined classical limit same way unequivocal criteria. We examine class collective spin models characterized by permutation symmetry spins. well-known Lipkin-Meshov-Glick (LMG) model is paradigmatic integrable system this limit. Thus, an excellent testbed for examining diagnostics. First, we calculate analytically EE Dicke basis{|j,m⟩}m=−jjin any bipartition, and show that thermodynamic limit, converges to1/2of maximal corresponding bipartition. Using finite-size scaling, numerically demonstrate aforementioned universal all parameter values LMG model. Our analysis illustrates how value far away from could signature integrability.