Abundance of Hard-Hexagon Crystals in the Quantum Pyrochlore Antiferromagnet

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