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

The phase diagram of the uniaxially anisotropic $s=1$ antiferromagnet on the kagome 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 two-dimensional 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 $s⩾2$ but then require strong on-site anisotropy in the Hamiltonian.

Figure 1

A portion of the kagome lattice, with the associated honeycomb lattice (dotted lines). For $0<D<J_z$, $J_{xy}=0$, and $T=0$, the three spins around every small triangle include one with $S_z=+1$, one with $S_z=-1$, and one with $S_z=0$. The bottom right shows breakup of a single bond defect into two vertex defects (large dots): the two defective vertices of the honeycomb lie on a loop containing only $S_z=0,+1$.

Figure 2

Phase diagram of spin-1 XXZ kagome antiferromagnet for fixed $D∊(0,J_z)$. The critical point $\mathbf{C}$ separates two distinct ordered phases $P_1$ and $P_2$ with sixfold symmetry breaking. The correlation length along the dotted line diverges as $T\to 0$ according to Eq. (6).