Abundance of hard-hexagon crystals in the quantum pyrochlore antiferromagnet

TL;DR

This paper introduces a family of valence-bond crystal ground states for the quantum pyrochlore antiferromagnet, characterized by exponential degeneracy and symmetry breaking, supported by variational and numerical methods.

Contribution

It proposes a novel class of valence-bond crystal ground states with exponential degeneracy and symmetry breaking, supported by variational, DMRG, and cluster expansion analyses.

Findings

Identifies a family of valence-bond crystals as ground states.

Demonstrates the stability of these states across related lattices.

Provides a variational wavefunction validated by numerical methods.

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.