Manipulable compact many-body localization and absence of superfluidity in geometrically frustrated systems

Geometric frustration is known to completely damage kinetic processes of some of the orbitals (and their associated quantum coherence) as to produce flat bands in the non-interacting systems. The impact of introducing additional interaction to the system in such frustrated systems is, however, a highly controversial issue. On the one hand, numerical studies on geometrically frustrated systems of hard-core boson (equivalent to a spin-1/2 systems) typically lead to glass or solid phases containing only local many-body coherence, indicating the persistence of the damage in quantum coherence. On the other, there continues to be noticeable claims of development of superfluidity that implies kinetic flow of particles. To resolve this apparent contradiction of great significance, we present a rigorous proof showing that density-density interaction is incapable of defeating the geometric frustration to allow propagation of those immobile particles, let alone sustaining a superfluidity. Instead, the frustrated systems develop many $\textit{compact}$ many-body localized states as "many-body scars" that do not thermalize, making them good candidates for storing $\textit{robust}$ and $\textit{manipulable}$ quantum information.