Valence Bond Crystal Ground State of the 1/9 Magnetization Plateau in the Spin-1/2 Kagome Lattice

Abstract

We investigate the ground state of a spin-1/2 kagome antiferromagnet at the 1/9 magnetization plateau, focusing primarily on six types of valence bond crystal (VBC) distortions. Among six types of VBC distortions, type 1 consistently exhibits the lowest ground-state energy. Analysis of the second derivative of the energy with respect to the distortion strength $J_{\mathrm{d}}$ using exact diagonalization reveals that, as the system size approaches the thermodynamic limit, the type 1 VBC state remains stable down to $J_{\mathrm{d}}=1$, corresponding to the undistorted kagome lattice. Perturbation theory further supports the stability of the type 1 VBC state, providing energy values that agree with exact diagonalization results within 3%. We also explore the possibility that other types of VBC distortions could become the ground state, but type 1 VBC still exhibited the lowest energy. These findings suggest that the ground state of the 1/9 plateau in the kagome lattice is the type 1 VBC state.

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• Recent progress in quantum spin liquids, fractional magnetization plateaus, and unconventional superconductivity in kagome lattices
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