Realization of fractonic quantum phases in the breathing pyrochlore lattice

Abstract

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.

11+12 pages, 8+7 figures, 2+4 tables; the first two authors contributed equally to this work

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• Human-machine collaboration: ordering mechanism of rank-2 spin liquid on breathing pyrochlore lattice
• Non-equilibrium dynamics of bosons with dipole symmetry: Large-$N$ Keldysh approach
• Breathing pyrochlore magnet CuGaCr${}_4$S${}_8$: Magnetic, thermodynamic, and dielectric properties
• Quantum lozenge tiling and entanglement phase transition
• Unconventional spin transport in strongly correlated kagome systems
• Anisotropic Spin Ice on a Breathing Pyrochlore Lattice
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice