Theory of the 1/9 Magnetization Plateau of the Spin-1/2 Kagome Heisenberg Antiferromagnet

Abstract

We investigate the 1/9 magnetization plateau of the spin-1/2 kagome Heisenberg antiferromagnet using infinite projected entangled-pair states and identify a spin-density-wave state with a $27$-site unit cell and a lower variational energy than previous approaches. In contrast to higher-magnetization plateaus, which are well described by localized magnons on nonoverlapping hexagons and preserve a sixfold rotational symmetry, the 1/9 plateau only keeps a threefold rotational symmmetry and consists of a tiling by three types of $9$-site clusters related by ±2π/3 rotations. These conclusions are supported by a complementary cluster mean-field theory which correctly preserves the symmetry of the higher plateaus but leads to the same spontaneous symmetry breaking for the 1/9 plateau with a qualitatively similar pattern of nine different local magnetizations.

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BibTeX

@misc{ghosh2026theory,
  title = {{Theory of the $1/9$ Magnetization Plateau of the Spin-$1/2$ Kagome Heisenberg Antiferromagnet}},
  author = {Pratyay Ghosh and Frédéric Mila},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.34439},
  eprint = {2610.34439},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.34439},
  note = {CC BY-SA 4.0},
}

RIS

TY  - UNPB
TI  - Theory of the 1/9 Magnetization Plateau of the Spin-1/2 Kagome Heisenberg Antiferromagnet
AU  - Pratyay Ghosh
AU  - Frédéric Mila
PY  - 2026
DA  - 2026/10/25
PB  - arXiv
DO  - 10.48550/arxiv.2610.34439
UR  - https://arxiv.org/abs/2610.34439
AB  - We investigate the 1/9 magnetization plateau of the spin-1/2 kagome Heisenberg antiferromagnet using infinite projected entangled-pair states and identify a spin-density-wave state with a $27$-site unit cell and a lower variational energy than previous approaches. In contrast to higher-magnetization plateaus, which are well described by localized magnons on nonoverlapping hexagons and preserve a sixfold rotational symmetry, the 1/9 plateau only keeps a threefold rotational symmmetry and consists of a tiling by three types of $9$-site clusters related by ±2π/3 rotations. These conclusions are supported by a complementary cluster mean-field theory which correctly preserves the symmetry of the higher plateaus but leads to the same spontaneous symmetry breaking for the 1/9 plateau with a qualitatively similar pattern of nine different local magnetizations.
ER  -

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