Mottness in obstructed atomic insulators without Mott transition

The obstructed atomic insulators are insulators with both atomic limits and boundary states. In this study, we examine the properties of obstructed atomic insulators under correlation. We utilize symmetry indicators by constructing many-body wave functions in momentum space. Our findings show that the obstruction properties, evidenced by boundary modes, persist even at high correlation levels (large U) where the charge freedom is strongly gapped. This suggests that the obstructed atomic insulator phase can seamlessly transition to its Mott phase without undergoing a Mott transition. Our analysis encompasses a variety of models, including the SuSchrieffer-Heeger chain, an anisotropic square lattice model, and the quadrupole insulator model.