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

Understand

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.