  The obstructed atomic insulators are insulators with both atomic limits and
boundary states. In this work, we study the obstructed atomic insulators under
correlation. We use the symmetry indicators by constructing many-body
wavefunctions in momentum space to prove the obstruction properties in
different models including the SSH chain, anisotropic square lattice model, the
quadrupole insulator model and etc. We demonstrate that the obstruction
properties with boundary modes persist at large $U$ where the charge freedom is
well-gapped, namely, this insulator phase can smoothly connect to its Mott
phase without Mott transition.
