Average Pure-State Entanglement Entropy in Spin 1/2 Systems with SU(2) Symmetry

Non-abelian symmetries play a central role in many areas in physics, and have been recently argued to result in distinct quantum dynamics and thermalization. Here we unveil the effect that the non-abelian SU(2) symmetry, and the rich Hilbert space structure that it generates for spin 1/2 systems, has on the average entanglement entropy of random pure states and of highly-excited Hamiltonian eigenstates. Focusing on the zero magnetization sector ( J z = 0 ) for different fixed spin J , we show that the entanglement entropy has a leading volume law term whose coefficient s A depends on the spin density j = 2 J/L , with s A ( j → 0) = ln 2 and s A ( j → 1) = 0 . We also discuss the behavior of the first subleading corrections.