Nature of the $1/9$ magnetization plateau of kagome antiferromagnets
In plain words
In a strong field the magnetization of a kagome antiferromagnet can stay fixed at one ninth of its maximum over a range of fields. Calculations disagree on whether this plateau state is a spin liquid with topological order or a regular crystal of spin pairs, and a 2024 experiment observed the plateau in a real compound.
Precise statement
Model: H = J sum_<ij> S_i . S_j - g mu_B H sum_i S^z_i, $S = 1/2$, kagome lattice, at magnetization $m = 1/9$ of saturation. Determine whether the plateau state is a $Z3$ topologically ordered spin liquid, a valence-bond crystal with an enlarged unit cell, or another state, and which describes the plateau observed in the yttrium-copper kagome hydroxybromide of Jeon et al. (Nature Physics 2024). An answer gives the classification with topological entanglement entropy or crystalline order parameters on cylinders of circumference at least 12 sites.
What would settle it
DMRG and tensor-network calculations that agree on topological entanglement entropy versus crystalline order at $m = 1/9$, compared with NMR lineshapes measured inside the plateau of the material.
Status in the literature
Unverified note
Jeon et al. (Nature Physics 2024) observed a $1/9$ plateau; numerical studies of the model disagree between a $Z3$ spin liquid and valence-bond crystals.