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

We investigate the effect that the non-Abelian SU(2) symmetry has on the average entanglement entropy of highly excited Hamiltonian eigenstates and of random pure states. Focusing on sectors with a fixed total spin (and zero total magnetization), we argue that the average entanglement entropy of highly excited eigenstates of quantum-chaotic Hamiltonians and of random pure states has a leading volume-law term whose coefficient is fixed by the appropriate dimension of the Hilbert space of the subsystem. While in the case of the highly excited eigenstates of integrable interacting Hamiltonians, we provide numerical evidence that the volume-law coefficient is smaller, which lends support to the expectation that the average eigenstate entanglement entropy can be used as a diagnostic of quantum chaos and integrability for Hamiltonians with non-Abelian symmetries. We also discuss the nature of the subleading corrections.

Reference: R. Patil, L. Hackl, G. R. Fagan, and M. Rigol, arXiv:2305.11211.