Eigenstate entanglement and thermalization with non-Abelian symmetries

Building on recent work extending the eigenstate thermalization hypothesis (ETH) to systems with SU(2) symmetry, we study eigenstates of chaotic Hamiltonians with global non-Abelian symmetries. We demonstrate in general how the ETH, including its extension via free probability and its relative, ergodic bipartition (EB), applies to systems whose global symmetries are described by semisimple Lie groups. Then focusing on the case of SU(2), we formulate a replica calculation to study the entanglement and thermodynamics of highly excited eigenstates. Among our results, we find a logarithmic correction to the Page curve and argue that this correction is a hallmark of non-Abelian symmetry.