Realization of fractonic quantum phases in the breathing pyrochlore lattice

Fractonic phases of matter are novel quantum ground states supporting subdimensional emergent excitations with mobility restrictions. Due to a subextensive ground state degeneracy that is dependent on the geometry of the underlying lattice, fractonic phases are considered as models for quantum memory or quantum glass. While there exist a number of exactly solvable models with interactions between multiple particles/spins, the realization of such models in real materials is extremely challenging. In this work, we provide a realistic quantum model of quadratic spin interactions on the breathing pyrochlore lattice of existing materials. We show that the emergent ``cluster charge'' excitations arise as vacuum fluctuations residing on the boundary of membrane objects, and move in a subdimensional space. Using the membrane operators, we demonstrate the existence of a subextensive ground state degeneracy explicitly depending on the lattice geometry, which is a useful resource for novel quantum memory.