The effect of SU(2) symmetry on many-body localization and thermalization

The many-body localized (MBL) phase is characterized by a complete set of quasi-local integrals of motion and area-law entanglement of excited eigenstates. We study the effect of non-Abelian continuous symmetries on MBL, considering the case of SU(2) symmetric disordered spin chains. The SU(2) symmetry imposes strong constraints on the entanglement structure of the eigenstates, precluding conventional MBL. We construct a fixed-point Hamiltonian, which realizes a non-ergodic (but non-MBL) phase characterized by eigenstates having logarithmic scaling of entanglement with the system size, as well as an incomplete set of quasi-local integrals of motion. We study the response of such a phase to local symmetric perturbations, finding that even weak perturbations induce multi-spin resonances. We conclude that the non-ergodic phase is generally unstable and that SU(2) symmetry implies thermalization. The approach introduced in this work can be used to study dynamics in disordered systems with non-Abelian symmetries, and provides a starting point for searching non-ergodic phases beyond conventional MBL.