Abundance of hard-hexagon crystals in the quantum pyrochlore antiferromagnet

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 wavefunction allows a precise determination of the energy, confirmed by DMRG 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.

6 pages, 4 papers, 13 pages supplementary material

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Cited by in corpus (12)

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• Thermodynamics of the $S=1/2$ hyperkagome-lattice Heisenberg antiferromagnet
• Single Crystal Diffuse Neutron Scattering Study of the Dipole-Octupole Quantum Spin Ice Candidate Ce${}_2$Zr${}_2$O${}_7$: No Apparent Octupolar Correlations Above $T=0.05$ K
• Classical spin models of the windmill lattice and their relevance for PbCuTe${}_2$O${}_6$
• DanceQ: High-performance library for number-conserving bases
• Phase diagram of the antiferromagnetic $J_1$-$J_2$ spin-$1$ pyrochlore Heisenberg model
• Quantum Spin Liquids Stabilized by Disorder in Non-Kramers Pyrochlores
• Thermodynamics of the Heisenberg antiferromagnet on the maple-leaf lattice
• Classification and correlation signatures of chiral spin liquids on the pyrochlore lattice
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice
• Simplex Crystal Ground State and Magnetization Plateaus in the Spin-$1/2$ Heisenberg Model on the Ruby Lattice