Realization of fractonic quantum phases in the breathing pyrochlore lattice

Fractonic phases of matter are novel quantum ground states supporting sub-dimensional emergent excitations with mobility restrictions. Due to a sub-extensive 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 sub-dimensional space. Using the membrane operators, we demonstrate the existence of a sub-extensive ground state degeneracy explicitly depending on the lattice geometry, which is a useful resource for novel quantum memory.