Eigenstate chaos in the presence of non-Abelian symmetries

The eigenstate thermalization hypothesis (ETH) posits that energy eigenstates encode local properties of the microcanonical ensemble. Motivated by recent interest in the physics of non-commuting conserved charges and the non-Abelian ETH, we study chaotic eigenstates in the presence of symmetries described by general compact Lie groups, such as SU(2). By applying non-Abelian symmetry resolution, we develop a non-Abelian microcanonical entropy and relate this entropy to the entanglement entropy of chaotic eigenstates. We find that microcanonical entropy is closely related to the symmetry-resolved entanglement entropy, which differs from conventional entanglement entropy by a universal logarithmic correction. Our results depend on the global Casimir charge, e.g. total spin. At finite charge density, we find a logarithmic enhancement to conventional entanglement entropy. At zero density, we find no such correction to entanglement entropy, but a logarithmic reduction to microcanonical entropy and symmetry-resolved entanglement entropy. We discuss the implications of our approach for non-Abelian eigenstate thermalization.