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Abundance of Hard-Hexagon Crystals in the Quantum Pyrochlore Antiferromagnet

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Schäfer,  Robin
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Placke,  Benedikt
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Benton,  Owen
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Moessner,  Roderich
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Schäfer, R., Placke, B., Benton, O., & Moessner, R. (2023). Abundance of Hard-Hexagon Crystals in the Quantum Pyrochlore Antiferromagnet. Physical Review Letters, 131(9): 096702. doi:10.1103/PhysRevLett.131.096702.


Cite as: https://hdl.handle.net/21.11116/0000-000D-ECAB-9
Abstract
We propose a simple family of valence-bond crystals as potential ground states of the S = 1/2 and S = 1 Heisenberg antiferromagnet on the pyrochlore lattice. Exponentially numerous in the linear size of the system, these can be visualized as hard-hexagon coverings, with each hexagon representing a resonating valence-bond ring. This ensemble spontaneously breaks rotation, inversion, and translation symmetries. A simple, yet accurate, variational wave function allows a precise determination of the energy, confirmed by the density matrix renormalization group and numerical linked cluster expansion, and extended by an analysis of excited states. The identification of the origin of the stability indicates applicability to a broad class of frustrated lattices, which we demonstrate for the checkerboard and ruby lattices. Our work suggests a perspective on such quantum magnets, in which unfrustrated motifs are effectively uncoupled by the frustration of their interactions.