Research: Hard-Hexagon Crystals in the Pyrochlore Antiferromagnet

One of the archetypal problems of frustration in three dimensions is the pyrochlore Heisenberg antiferromagnet, a system that gives rise to unconventional phases of matter extending beyond traditional order. Despite decades of intensive research, this model has proven elusive for many theoretical approaches, and numerous fundamental questions remain unanswered. By employing a generalized cluster expansion, we have unlocked a novel perspectives into its properties at zero temperature. While prior studies predominantly centered on the frustrated tetrahedral structure, our focus shifted towards unfrustrated hexagonal loops, exploring the possibility of a hard-hexagon ground state in the quantum realm. A generalized cluster expansion enables us to construct variational states describing the new family of valence-bond crystals that is exponentially large in the linear size of the system as potential ground states.

R. Schäfer, B. Placke, O. Benton, R. Moessner,
Abundance of Hard-Hexagon Crystals in the Quantum Pyrochlore Antiferromagnet,
Phys. Rev. Lett. 131, 096702 (2023) (arXiv)