  Recently a class of quantum systems exhibiting weak ergodicity breaking has
attracted much attention. These systems feature a special band of eigenstates
called quantum many-body scar states in the energy spectrum. In this work we
study the fate of quantum many-body scar states in a two-dimensional lattice
against random disorders. We show that in both the square lattice and the
honeycomb lattice the scar states can persist up to a finite disorder strength,
before eventually being killed by the disorder. We further study the
localization properties of the system in the presence of even stronger
disorders and show that whether a full localization transition occurs depends
on the type of disorder we introduce. Our study thus reveals the fascinating
interplay between disorder and quantum many-body scarring in a two-dimensional
system.
