Geometric criticality between plaquette phases in integer-spin kagome XXZ antiferromagnets

TL;DR

This paper explores a unique geometric critical line in the phase diagram of an $s=1$ kagome antiferromagnet, revealing unconventional plaquette-ordered phases and their finite-temperature correlations through a three-color model mapping.

Contribution

It introduces a novel geometric criticality in $s=1$ kagome antiferromagnets, distinct from classical limits, and connects these phases to known models like the honeycomb dimer and $s=1/2$ $XXZ$ models.

Findings

Critical line described by the three-color model.

Unconventional plaquette-ordered phases with sixfold symmetry breaking.

Finite-temperature correlations and phase transition characteristics elucidated.

Abstract

The phase diagram of the uniaxially anisotropic $s=1$ antiferromagnet on the kagom\'e lattice includes a critical line exactly described by the classical three-color model. This line is distinct from the standard geometric classical criticality that appears in the classical limit ($s \to \infty$) of the 2D XY model; the $s=1$ geometric T=0 critical line separates two unconventional plaquette-ordered phases that survive to nonzero temperature. The experimentally important correlations at finite temperature and the nature of the transitions into these ordered phases are obtained using the mapping to the three-color model and a combination of perturbation theory and a variational ansatz for the ordered phases. The ordered phases show sixfold symmetry breaking and are similar to phases proposed for the honeycomb lattice dimer model and $s=1/2$ $XXZ$ model. The same mapping and phase transition can be realized also for integer spins $s \geq 2$ but then require strong on-site anisotropy in the Hamiltonian.