Many-body localization (MBL) provides a mechanism to avoid thermalization in many-body
quantum systems. Here, we show that an emergent symmetry can protect a state from MBL.
Specifically, we propose a Z2 symmetric model with nonlocal interactions, which
has an analytically known, SU(2) invariant, critical ground state. At large disorder strength, all
states at finite energy density are in a glassy MBL phase, while the lowest energy states are not.
These do, however, localize when a perturbation destroys the emergent SU(2) symmetry. The
model also provides an example of MBL in the presence of nonlocal, disordered interactions that
are more structured than a power law. Finally, we show how the protected state can be moved
into the bulk of the spectrum.
Phys. Rev. Lett. 125, 240401 (2020)